Random Processes in Physics and Finance

Random Processes in Physics and Finance

Volumn , Issue , 2010, Pages 1-344

  Lax, Melvin ^a   Cai, Wei ^a   Xu, Min ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Boltzmann transport equation; Delta functions; Fluctuation dissipation theorem; Fokker planck process; Langevin equation; Noise; Probability theory; Random processes

Indexed keywords

EID: 84921858924     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1093/acprof:oso/9780198567769.001.0001     Document Type: Book

References (264)

1. Abramatic, J. F. and Silverman, L. M. (1982). Nonlinear restoration of noisy images. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAM1-4, No. 2, 141-148.
2. Alexander, H. W. (1961). Elements of Mathematical Statistics. John Wiley and Sons, New York.
3. Alfano, R. R. ed. (1994). OSA Proceedings on Advances in Optical Imaging and photon Migration. Optical Soceity of America, Washington D.C.
4. Anis, A. A. and Lloyd, E. H. (1976). The expected value of the adjusted rescaled hurst range of independent normal summands. Biometrika, 63, p111-116.
5. Arfken, G. B. and Weber, H. J. (1995). Mathematical Methods for Physicists. Academic Press, San Diego.
6. Backus, G. and Gilbert, F. (1970). Uniqueness of the inversion of inaccurate gross earth data. Philosophical Transactions of the Royal Society, 256, 123-192.
7. Bayes, T. (1763). Essay towards solving a problem in the doctrine of chance. Philosophical Transactions of the Royal Society, Essays LII, 370-418.
8. Bell, D. A. (1960). Electrical Noise. Van Nostrand. London.
9. Bellman, R. E. (1964). Invariant Embedding and Time-independent Transport Processes. American Elsevier Pub. Co., New York.
10. Bellman R. and Wing G. (1976). An Introduction to Invariant Embedding. Wiley, New York.
11. Bendat, J. S. and Piersol, A. G. (1971). Random Data: Analysis and Measurement Process. Wiley, New York.
12. Benjamin, R. (1980). Generalization of maximum-entropy pattern analysis. IEEE Proceedings, 127 pt F, 341-353.
13. Bernstein, P. L. (1998). Against the Gods, the Remarkable Study of Risk. Wiley, New York.
14. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654.
15. Bouchard, J. and Sornette, D. (1994). The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes. Journal de Physique I (Paris), 4, 863-881.
16. Brillinger, D. R. and Krishnaiah, P. R. (1983). Handbook of Statistics III. North Holland, Amsterdam.
17. Brockwell, P. J. and Davis R. A. (1991). Time Series Theory and Methods. Springer Verlag, New York.
18. Brown, R. (1828). A brief account of microscopical observations made in the months of June, July, and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. The Philosophical Magazine, 4, 161-173.
19. Bullard, B. C. and Cooper, R. J. B. (1948). The determination of the masses necessary to produce a given gravitational field. Proceedings of the Royal Society A (London), 194, 332-347.
20. Burgess, R. E. (1965). Fluctuation Phenomena in Solids. Academic Press, New York.
21. Cai, W., Lax, M., and Alfano, R. R. (2000a). Cumulant solution of the elastic Boltzmann transport equation in an infinite uniform medium. Physcial Review E, 61, 3871-3876.
22. Cai, W., Lax, M., and Alfano, R. R. (2000b). Analytical solution of the elastic Boltzmann transport equation in an infinite uniform medium using cumulant expansion. Journal of Physical Chemistry B, 104, 3996-4000.
23. Cai, W., Lax, M., and Alfano, R. R. (2000c). Analytical solution of the polarized photon transport equation in an infinite uniform medium using cumulant expansion. Physical Review E, 63, 016606.
24. Cai, W., Xu, M., Lax, M., and Alfano, R. R. (2002). Diffusion coefficient depends on time not on absorption. Optics Letters, 27, 731-733.
25. Cai, W., Xu, M., and Alfano, R. R. (2003). Three-dimensional radiative transfer tomography for turbid media. IEEE Selected Topics in Quantum Electronics, 9, 189-198.
26. Cai, W., Xu, M., and Alfano, R. R. (2005). Analytical form of the particle distribution based on the cumulant solution of the elastic Boltzmann transport equation. Physical Review E, 71, 041202.
27. Callen, H. B. and Welton, T. A. (1951). Irreversibility and generalized noise. Physical Review, 83, 34-40.
28. Callen, H. B. and Greene, R. F. (1952). Theorem of irreversible thermodynamics. Physical Review, 86, 704-710.
29. Cameron, R. H. and Martin, W. T. (1944). The Wiener measure of Hilbert neighborhoods in the space of continuous functions. Journal Mathematical Physics, 23, 195-209.
30. Cameron, R. H. and Martin, W. T. (1945). Transformations of Wiener integrals under a general class of linear transformations. Transactions of the American Mathematical Society, 58, 184-219.
31. Campbell, N. (1909). The study of discontinuous phenomena. Proceedings of the Cambridge Philosophical Society, 15, 117-136.
32. Carley, A. E. and Joyner, R. W. (1979). The application of deconvolution methods in electron spectroscopy - a review. Journal of Electron Spectroscopy and Related Phenomena, 16, 1-23.
33. Casimir, H. B. and Polder, D. (1948). The influence of retardation on the London-van der Waals forces. Physical Review, 73, 360-372.
34. Cercignani, C. (1988). The Boltzmann Equation and its Applications. Series in Applied Mathematical Sciences, Springer-Verlag, New York.
35. Chan, H. B., Aksyuk, V. A., Kleiman, R. N., Bishop, D. J., and Capasso, F. (2001). Quantum mechanical actuation of microelectromechanical systems by the Casimir force. Science, 291, 1941-1944.
36. Chandrasekhar, S. (1943). Stochastic problems in physics and astronomy. Reviews of Modern Physics, 15, 1-89.
37. Chandrasekhar, S. (1960). Radiative Transfer. Dover, New York.
38. Chung, K. L. (1968). A Course in Probability. Harcourt Brace and World, New York
39. van Cittert, P. H. (1931). Zum einfluss der spaltbreite auf die intensitatsverteilung in spektrallinien. Zeitschrift für Physik, 69, 298-308.
40. Cohen, L. (1995). Time-Frequency Analysis. Prentice Hall, New Jersey.
41. Dahlquist, G. and Bjorck, A. (1974). Numerical Methods. Prentice Hall, New Jersey.
42. Demoment G. (1989). Image reconstruction and restoration: Overview of common estimation structures and problems. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37, 2024-2036.
43. Deryagin, B. V. and Abrikosova, I. I. (1956). Direct measurement of molecular attraction of solid bodies. I. Statement of the problem and methods of measurement of forces using negative feedback. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 30, 993-1006.
44. Deryagin, B. V., Abrikosova, I. I., and Lifshitz, E. M. (1956). Direct measurement of molecular attraction between solids separated by a narrow gap. Quarterly Reviews -Chemical Society (London), 10, 295-329.
45. Deutch, R. (1962). Nonlinear Transformations of Random Processes. Prentice Hall. New Jersey.
46. Dirac, P. A. M. (1935). Principles of Quantum Mechanics. Oxford, New York.
47. Doob, J. L. (1942). The Brownian motion and stochastic equations. Annals of Mathematics, 43, 351-369.
48. Doob, J. L. (1953). Stochastic Processes. Wiley, New York.
49. Durduran, T., Yodh, A. G., Chance, B., and Boas, D. A. (1997). Does the photon-diffusion coefficient depend on absorption? Journal of the Optical Society of America A, 14, 3358- 3365.
50. Dyson, F. (1949). The S matrix in quantum electrodynamics. Physical Review, 75, 1736- 1755.
51. Dyson, F. (1949). The radiation theories of Tomonaga, Schwinger and Feynman. Physical Review, 75, 486-502.
52. Eberhard, A. (1973). An optimum discrete window for the calculation of power spectra. IEEE Transactions on Audio and Electroacoustics, 21, 37-43.
53. Eberly, J. H. and W'odkiewicz, K. (1977). The time-dependent physical spectrum of light. Journal of the Optical Society of America, 67, 1252-1261.
54. Einstein, A. (1905). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat. Annalen der Physik, 17, 549-560.
55. Einstein, A. (1906). On the theory of the Brownian movement. Annalen der Physik, 19, 371-381.
56. Einstein, A. (1956). Investigations on the Theory of the Brownian Movement. Dover, New York.
57. Ekstein, H. and Rostoker, N. (1955). Quantum theory of fluctuations. Physical Review, 100, 1023-1029.
58. Fadeeva, V. N. (1959) Computational Methods of Linear Algebra. Dover, New York.
59. Feller, W. (1957, 1971). An Introduction to Probability Theory and its Applications. Volume I and II. Wiley, New York.
60. Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20, 367-398.
61. Feynman, R. P. (1951). An operator calculus having applications in quantum electrodynamics. Physical Review, 84, 108-128.
62. Ford, G. W. and O'Connell, R. F. (1996). There is no quantum regression theorem. Physical Review Letters, 77, 798-801.
63. Ford, G. W. and O'Connell, R. F. (2000). Driven system and the Lax formula. Optics Communications, 179, 451-461.
64. Fox, P. A., Hall, A. D., and Schryer, N. L. (1978a). The PORT Mathematical Subroutine Library. ACM Transactions on Mathematical Software, 4, 104-126.
65. Fox, P. A., Hall, A. D., and Schryer, N. L. (1978b). Algorithm 528: framework for a portable library. ACM Transactions on Mathematical Software, 4, 177-188.
66. Franklin, J. N. (1970). Well-posed stochastic extensions of ill-posed linear problems. Journal of Mathematical Analysis and Applications, 31, 682-716.
67. Freeman, J. J. (1952). On the relation between the conductance and the noise power of certain electronic streams. Journal of Applied Physics, 23, 1223-1225.
68. Frieden, B. R. (1975). Image enhancement and restoration in Topics in Applied Physics, ed. Huang, T. S. Springer-Verlag, New York.
69. Fry, T. C. (1925). The theory of the schroteffekt. Journal of the Franklin Institute, 199, 203-220.
70. Fry, T. C. (1928). Probability and its Engineering Uses. Van Nostrand, London.
71. Furth, R. (1920). Die brownsche bewegung bei berücksichtigung einer persistenz der bewegungsrichtung mit anwendungen auf die bewegung lebender infusorien. Zeitschrift für Physik A, 2, 244-256.
72. Furth, R. (1922). Die bestimmung deer elektronenladung aus dem schroteffekt an gluhkathodenrohren. Physikalische Zeitschrift, 23, 354-362.
73. Gandjbakhche, A. H. ed. (1999). Proceedings of Inter-Institute Workshop on in-vivo Optical Imaging at the NIH, Optical Soceity of America, Washington D.C.
74. Gardiner, W. A. (1992). Fundamental comparison of Fourier transformation and model fitting methods of spectral analysis. Imaging Systems and Technology, 4, 109-121.
75. Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., and Dodge, Y. (1996). Turbulent cascades in foreign exchange markets. Nature, 381, 767-770.
76. Glauber, R. J. (1963a). Photon correlations. Physical Review Letters, 10, 84-86.
77. Glauber, R. J. (1963b). The quantum theory of optical coherence. Physical Review, 130, 2529-2539.
78. Glauber, R. J. (1963c). Coherent and incoherent states of the radiation field. Physical Review, 131, 2766-2788.
79. Glauber, R. J. (1965). Optical coherence and photon statistics in Quantum Optics and Electrons, eds. DeWitt, C., Blandin, A., Cohen-Tannoudji, C., Gordon and Breach, New York.
80. Goldstein, H. (1980). Classical Mechanics. Addison-Wesley, New York.
81. Goursat, E. (1917). Differential Equations. Ginn and Co., Boston.
82. Greene, R. F. and Callen, H. B. (1952). Theorem of irreversible thermodynamics II. Physical Review, 88, 1387-1391.
83. Grobner, W. and Hofreiter, N. (1950). Integraltafel, Bestimmte Integrate. Springer Verlag, Berlin.
84. Hamming, R. W. (1991). The Art of Probability. Addison Wesley, New York.
85. Harris, F. J. (1978). On the use of windows for harmonic analysis with discrete Fourier transform. Transactions of IEEE, 66, 51-53.
86. Hartmann, C. A. (1921). The determination of the elementary electric charge by means of the "shot effect". Annalen der Physik, 65, 51-78.
87. Harris, B. (1967). Spectral Analysis of Time Series, John Wiley, New York.
88. Hassan, T. (1983). Complex demodulation: some theory and applications in Handbook of Statistics III, eds. D. Brillinger and P. Krishnaiah. North Holland, Amsterdam.
89. Hashitsume, N. (1956). A statistical theory of linear dissipative systems, II. Progress of Theoretical Physics, 15, 369-413.
90. Hauge, E. H. (1974). What can we learn from Lorentz models? in Transport phenomena, 337-367, Springer-Verlag, Berlin.
91. Hempstead, R. D. and Lax, M. (1967CVI). Classical noise VI: noise in self-sustained oscillators near threshold. Physical Review, 161, 350-366.
92. Hill, J. E. and van Vliet, K. M. (1958). Ambipolar transport of carrier density fluctuations in germanium. Physica, 24, 709-720.
93. Hillary, D. J., Wark, D. Q., and James D. G. (1965). An experimental determination of the atmospheric temperature profile by indirect means. Nature, 205, 489-491.
94. Hull, A. W. and Williams, N. H. (1925). Determination of elementary charge e from measurements of shot-effect. Physical Review, 25, 147-173.
95. Hull, J. (1989, 2001). Options, Futures and other Derivative Securities. Prentice Hill, New Jersey.
96. Hurst, H. E. (1951). Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770-799.
97. IMSL Inc. (1987). IMSL Math/Library Users Manual. IMSL, Houston.
98. Ishimaru, A. (1978). Wave Propagation and Scattering in Random Media, Volume I and II. Academic, New York.
99. Ito, K. (1951). On stochastic differential equations. Memoirs of the American Mathematical Society, 4, 1-51.
100. Ito, K. and McKean, H. P. (1965). Diffusion Processes and their Sample Paths. Academic Press, New York.
101. Jackson, J. D. (1975). Classical Electrodynamics. Wiley, New York.
102. Jansson, P. A., Hunt, R. H. and Plyler, E. K. (1970). Resolution enhancement of spectra. Journal of the Optical Society of America, 60, 596-599.
103. Jansson, P. A. (1970). Method for determining the response function of a high-resolution infra-red spectrometer. Journal of the Optical Society of America, 60, 184-191.
104. Jansson, P. A., Hunt, R. H. and Plyler, E. K. (1970). Resolution enhancement of spectra. Journal of the Optical Society of America, 60, 596-599.
105. Jaynes, E. T. (1958). Probability Theory in Science and Engineering. Socony Mobil Oil Co., Dallas.
106. Jeffries, H. and Jeffreys, B. S. (1950). Methods of Mathematical Physics. Cambridge University Press, London.
107. Jeffreys, H. (1957). Scientific Inference. Cambridge University Press, London.
108. John, F. (1955). Numerical solution of the equation of heat conduction for proceeding times. Annali di Matematica Pura ed Applicata, 4, 129-142.
109. Johnson, J. B. (1928). Thermal agitation of electricity in conductors. Physical Review, 32, 97-109.
110. Kac, M. and Siegert, A. J. F. (1947). On the theory of noise in radio receivers with square law detectors. Journal of Applied Physics, 18, 383-400.
111. Kahaner, D., Moler, C., and Nash, S. (1989). Numerical Methods and Software, Prentice Hall, New Jersey.
112. van Kampen N. (1992). Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam.
113. Kaplan, L. D. (1959). Inferences of atmospheric structures from satellite remote radiation measurements. Journal of the Optical Society of America, 49, 1004-1014.
114. Karhunen, K. (1946). Zur spektraltheorie stochastischer prozesse. Annales Academiae Scientiarum Fennicae, 37.
115. Kelley, P. L. and Kleiner, W. V. (1964). Theory of electromagnetic field measurement and photoelectron counting. Physical Review, 136, A316-A334.
116. Kendall, M. G. (1999). Kendall's Advanced Theory of Statistics. Oxford University Press, London.
117. Kendall, M. G. and Stuart, A. (1969). The Advanced Theory of Statistics. Volume I. Hafner, New York.
118. Khinchine, A. (1934). Korrelationstheorie de stationaren stochastichen prozesse. Mathematische Annalen, 109, 604-615.
119. Khinchine, A. (1938). The theory of stationary chance processes. Rossiĭskaya Akademiya Nauk, 5.
120. Kitchener, J. A. and Prosser, A. P. (1957). Direct Measurement of the long-range van der Waals forces. Proceedings of the Royal Society of London. A, 242, 403-409.
121. Kittel, C. (1958). Elementary Statistical Physics. John Wiley, New York.
122. Kleiner, B., Martin, R. D., and Thomson, D. J. (1979). Robust estimation of power spectra. Journal of the Royal Statistical Society B, 41, 313-351.
123. Kolmogorov, A. N. (1950). Foundations of the Theory of Probability, Chelsea, New York (a translation of the 1933 Russian version).
124. Kuo, C., Lindberg, C. R., and Thomson, D. J. (1990). Coherence established between atmospheric carbon dioxide and global temperature. Nature, 343, 709-714.
125. Kubo, R. (1957). Statistical mechanical theory of irreversible processes I. Journal of the Physical Society of Japan, 12. 570-586.
126. Kubo, R. (1962). Generalized cumulant expansion method. Journal of the Physical Society of Japan, 17, 1100-1120.
127. Kyburg, H. E. (1969). Probability Theory. Prentice Hall, New Jersey.
128. Lampard, D. G. (1954). Generalization of the Wiener-Khintchine theorem to nonstationary processes. Journal of Applied Physics, 25, 802-803.
129. Langevin, M. P. (1908). Sur la thÃl'orie du mouvement brownien. Comptes-Rendus de l'AcadÃl'mie des Sciences (Paris), 146, 530-533.
130. Lawson, J. L. and Uhlenbeck, G. E. (1950). Threshold Signals, MIT Radiation Lab Series, 24, McGraw Hill, New York.
131. Lax, M. and Phillips, J. C. (1958). One dimensional impurity bands. Physical Review, 110, 41-49.
132. Lax, M. (1958QI). Generalized mobility theory. Physical Review, 109, 1921-1926.
133. Lax, M. and Mengert, P. (1960). Influence of trapping, diffusion and recombination on carrier concentration fluctuations. Journal of Physics and Chemstry of Solids, 14, 248- 267.
134. Lax, M. (1960I). Fluctuations from the nonequilibrium steady state. Reviews of Modern Physics, 32, 25-64.
135. Lax, M. (1963QII). Formal theory of quantum fluctuations from a driven state. Physical Review, 129, 2342-2348.
136. Lax, M. (1964QIII). Quantum relaxation, the shape of lattice absorption and inelastic neutron scattering lines. Journal of Physics and Chemistry of Solids, 25, 487-503.
137. Lax, M. (1966III). Classical noise III: nonlinear via Markoff processes. Reviews of Modern Physics, 38, 359-379.
138. Lax, M. (1966IV). Classical noise IV: Langevin methods. Reviews of Modern Physics, 38, 541-566.
139. Lax, M. (1966QIV). Quantum noise IV: quantum theory of noise sources. Physical Review, 145, 110-129.
140. Lax, M. (1967). Quantum theory of noise in masers and lasers. in 1966 Tokyo Summer Lecture in Theoretical Physics, Part 1: Dynamical Processes in Solid State Optics, eds. Kubo, R. and Kamimura, H., Benjamin, New York, 195-245.
141. Lax, M. (1967V). Classical noise V: noise in self sustained oscillators. Physical Review, 160, 290-307.
142. Lax, M. (1968). Fluctuations and coherence phenomena in classical and quantum physics in 1966 Brandeis Summer Lecture Series, Statistical Physics, volume 2, eds. Chretien, M., Gross, E. P., and Deser, S., Gordon and Breach Science Publishers, New York, 270-478.
143. Lax, M. (1968QXI). Quantum noise XI: multitime correspondence between quantum and classical stochastic processes. Physical Review, 72, 350-361.
144. Lax, M. and Yuen, H. (1968). Quantum noise XIII: six classical variable description of quantum laser fluctuations. Physical Review, 172. 362-371.
145. Lax, M. and Zwanziger, M. (1973). Exact photocount statistics: lasers near threshold. Physical Review A, 7, 750-771.
146. Lax, M. (1974). Symmetry Principles in Solid State and Molecular Physics. John Wiley and Sons, New York.
147. Lax M. (1997). Stochastic processes. Encyclopedia of Applied Physics, 20, 19-60.
148. Lax, M. (2000). The Lax-Onsger regression 'theorem' revisited. Optics Communications, 179, 463-476.
149. Levinson, N. (1947). A heuristic derivation of Wiener's mathematical theory of prediction and filtering. Journal of Mathematics and Physics, 26, 110-119.
150. Louisell, W. H. (1973). Quantum Statistical Properties of Radiation. Wiley, New York.
151. Lukacs, E. (1960). Characteristic Functions. Griffith, London.
152. MacDonald, D. K. C. (1962). Noise and Fluctuations. Wiley, New York.
153. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. Freeman, San Francisco.
154. Mandelbrot, B. B. (1997). Fractals and Scaling in Finance. Springer, Berlin.
155. Merton, R. C. (1973). Theory of rational pricing. Bell Journal of Economics and Management Science, 4, 141-183.
156. Middleton, D. (1960). Introduction to Statistical Communication Theory. McGraw-Hill, New York.
157. von Mises, R. (1937). Probability Statistics and Truth, 2nd edn. Macmillan, New York.
158. Montroll, E. W. (1952). Markoff chains, Wiener integrals, and quantum theory. Communications in Pure and Applied Mathematics, 5, 415-453.
159. Montroll, E. and Shlesinger, M. (1983). A wonderful world of random walks. in CCNY Physics Symposium in Celebration of Melvin Lax's Sixtieth Birthday, City College of New York, New York.
160. Moran, P. A. P. (1968). An Introduction to Probability Theory. Clarendon, Oxford.
161. Morse, P. and Feshbach H. (1953). Methods of Theoretical Physics. McGraw-Hill, New York.
162. Moullin, E. B. (1938). Spontaneous Fluctuation of Voltage. Oxford, New York.
163. Moyal, J. E. (1949). Quantum mechanics as a statistical theory. Proceedings of the Cambridge Philosophy Society, 45, 99-124.
164. Murdoch, J. B. (1970). Network Theory. McGraw-Hill, New York.
165. NAG Fortran Liboratory. Numerical Analysis Group.
166. von Nageli, K. (1879). Sitzber, Kgl. Bayerische Akad. wiss. Munchen, Math-Physik Kl 9, 389-453.
167. Nielsen, L. T. (1999). Pricing and Hedging of Derivative Securities. Oxford University Press, London.
168. Noble, B. (1977). The Numerical solution of IEs. in The State of the Art in Numerical Analysis, ed. D. Jacobs, Academic Press, London.
169. North, D. O. (1940). Fluctuations in space charge limited currents at moderately high frequencies. part II: diodes and negative grid triodes. RCA Review, 4, 441.
170. Nyquist, H. (1927). Minutes of the New York meeting, February 25-26, 1927. Joint meeting with the Optical Society of American. Physical Review, 29, 614.
171. Nyquist, H. (1928). Thermal agitation of electric charge in conductors. Physical Review, 32, 110.
172. Onsager, L. (1931a). Reciprocal relations in irreversible processess. I. Physical Review, 37, 405-426.
173. Onsager, L. (1931b). Reciprocal relations in irreversible processess. II. Physical Review, 38, 2265-2279.
174. Page, C. H. (1952). Instantaneous power spectra. Journal of Applied Physics, 23, 103- 106.
175. Papoulis, A. (1973). Minimum bias windows for high resolution spectrum estimates. IEEE Transactions on Information Theory, 19, 9-12.
176. Parzen, E. (1960). Modern Probability Theory and Its Applications. John Wiley, New York.
177. Pawula, R. F. (1967). Approximation of the linear Boltzmann equation by the Fokker-Planck equation. Physical Review, 162, 186-188.
178. Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine B, 50, 7.
179. Percival, D, B. and Walden, A. T. (1993). Spectral Analysis for Physical Applications. Cambridge University Press, London.
180. Peters, E. E. (1994). Fractal Market Analysis. Wiley, New York.
181. Phillips, D. L. (1962). A technique for the numerical solution of certain integral equations of the first kind. Journal of Association for Computing Machinery, 9, 84-97.
182. de-Picciotto, R., Reznikov, M., Heilblum, M., Umansky, U., Bunun, G., and Mahalu, D. (1997). Direct observation of a fractional charge. Nature, 389, 162.
183. de-Picciotto, R. (1998). Shot noise of non-interacting composite Fermions. Preprint Weizman Institute of Science, Talk at Bell Laboratories, 03/02/1998.
184. PORT (1984). PORT Mathematical Subroutine Library. Bell Labs, New Jersey.
185. Power, E. A. (1964). Introductory Quantum Electrodynamics. Longmans, Green and Co., London.
186. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes in Fortran, 2nd edn. Cambridge University Press, London.
187. Price, G. L. (1982). Isolation of instability in the Fredholm integral equation of the first kind: application to the deconvolution of noisy spectra. Journal of Applied Physics, 53, 4571-457.
188. Priestley, M. B. (1981). Spectral Analysis and Time series. Academic Press, London.
189. Rack, A. J. (1938). Effect of space charge and transit time on shot noise in diodes. Bell System Technical Journal, 17, 592.
190. Ramsey, J. B. and Thomson, D. J. (1999). A reanalysis of the spectral properties of some economic and financial time series. in Nonlinear Time Series Analysis of Economic and Financial Data, ed. Rothman, P., Kluwer Academic Publishers, New York.
191. Reggiani, L., Lugli, P., and Mitin, V. (1988). Generalization of Nyquist-Einstein relationship to conditions far from equilibrium in nondegenerate semiconductors. Physical Review Letters, 60, 736.
192. Rice, S. O. (1944). Mathematical analysis of random noise, part I: shot noise. Bell System Technical Journal, 23, 282-310.
193. Rice, S. O. (1945). Mathematical analysis of random noise, part II: power spectra and correlation functions. Bell System Technical Journal, 24, 46-70.
194. Rice, S. O. (1948a). Mathematical analysis of random noise, part III: statistical properties of random noise currents. Bell System Technical Journal, 27, 109.
195. Rice, S. O. (1948b). Mathematical analysis of random noise, part IV: noise through nonlinear devices. Bell System Technical Journal, 27, 115.
196. Risken, H. and Vollmer, H. D. (1967). Correlation of the amplitude and of the intensity fluctuation near threshold. Zeitschrift für Physik, 181, 301-312.
197. Robinson, F. N. H. (1962). Noise in Electric Circuits. Clarendon, Oxford.
198. Robinson, F. N. H. (1974). Noise and Fluctuations in Electronic Devices and Circuits. Clarendon, Oxford.
199. van Roosebroeck, W. (1953). Transport of added current carriers in a homogenous semiconductors. Physical Review, 91, 282-289.
200. Schawlow, A. L. and Townes, C. H. (1958). Infrared and optical masers. Physical Review, 112, 1940.
201. Scher, H. and Lax, M. (1973). Stochastic transport in a disordered solid. I. theory. Physical Review B, 7, 4491-4502.
202. Schottky, W. (1918). Uber spontane Stromschwankungen in verschiednen Elektrizitatsleitern. Annalen der Physik, 57, 541-567.
203. Schuster, A. (1898). On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terestrial Magnetism, 3, 13-41.
204. Scully, M. O. and Lamb, W. E. (1967). Quantum theory of an optical meser. I. general theory. Physical Review, 159, 208-226.
205. Scully, M. O. and Lamb, W. E. (1969). Quantum theory of an optical maser. III. theory of photoelectron counting statistics. Physical Review, 179, 368.
206. Scully, M. O. and Zubairy, M. S. (1995). Quantum Optics. Cambridge University Press., London.
207. Shaw, C. B. Jr. (1972). Improvement of the numerical resolution of an instrument by numerical solution of the integral equation. Journal of Mathematical Analysis and Applications, 37, 83-112.
208. Shlesinger, M. F. (1996). Random processes. Encyclopedia of Applied Physics, 16, 45-70.
209. Shockley, W. (1938). Currents to conductors induced by a moving point charge. Journal of Applied Physics, 9, 635-636.
210. Shockley, W. (1950). Electrons and Holes in Semiconductors, Van Nostrand, London.
211. Shockley, W., Copeland, J. A., and James, R. P. (1966). The impedance field method of noise calculation in active semiconcuctor devices. in Quantum Theory of Atoms, Molecules and the Solid State, ed. Lowdin, P. O., Academic Press, New York, 537-563.
212. Slepian, D. and Pollak, H. (1961). Prolate spheroidal wave functions, Fourier analysis and uncertainty. Bell System Techcal Journal, 40, 43-64.
213. Slepian, D. (1964). Prolate spheroidal wave functions, Fourier analysis and uncertainty IV. Bell System Technical Journal, 43, 3009-3057.
214. Slepian, D. (1965). Some asymptotic expansions for prolate spheroidal wave functions. Journal of Mathmatical Physics, 44, 99-140.
215. Slepian, D. (1978). Prolate spheroidal wave functions, Fourier analysis and uncertainty V:the discrete case. Bell System Technical Journal, 57, 1371-1429.
216. Smith, W. A. (1974). Laser intensity fluctuations when the photon number at threshold is small. Optics Communications, 12, 236-239.
217. Smoluchowski, M. V. (1916). Drei Vortrage uber Diffusion, Brownische Bewegung und Koagulation von Kolloidteilchen. Physik Zeitschrift, 17, 557, 585.
218. Stratonovich, R. L. (1963). Topics in the Theory of Random Noise, Vol. I. Gordon and Breach, New York.
219. Thiele, T. N. (1903). Theory of Observations, Dayton, Londons. Reprinted in Annals of Mathematical Statistics, 2, (1931), 165-308.
220. Thomson, D. J. (1977). Spectrum estimation techniques for characterization and development of WT4 waveguide. Bell System Technical Journal, 56, Part I, 1769-1815; Part II, 1983-2005.
221. Thomson, D. J. (1982). Spectrum analysis and harmonic analysis. Proceedings IEEE (special issue on spectrum estimation), 70, 1055-1096.
222. Thomson, D. J. (1990a). Time series analysis of holocene climate data. Philosophical Transactions of the Royal Society of London Series A, 330, 601-616.
223. Thomson, D. J. (1990b). Quadratic-inverse spectrum estimates; applications to paleoclimatology. Philosophical Transactions of the Royal Society of London Series A, 332, 539-597.
224. Thomson, D. J. and Chave, A. D. (1991). Jackknifed error estimates for spectra, coherences, and transfer functions in Advances in Spectrum Estimation, ed. Haykin S., Prentice Hall, New Jersey, 58-113.
225. Thomson, D. J. (1995). The seasons, global temperature, and precession. Science, 268, 59-68.
226. Thomson, D. J., MacLennan, C. G., and Lanzerotti, L. J. (1995). Propagation of solar oscillations through the interplanetary medium. Nature, 376, 139-144.
227. Thomson, D. J. (1997). Dependence of global temperatures on atmospheric CO2 and solar irradiance. Proceedings of the National Academy of Sciences of the United States of America, 94, 8370-8377.
228. Thomson, D. J. (2001). Multitaper analysis of nonstationary and nonlinear time series data. Nonlinear and Nonstationary Signal Processing, eds. Fitzgerald, W., Smith, R., Walden, A., and Young, P., Cambridge University Press, London, 317-394.
229. Thornber, K. K. (1974). Treatment of microscopic fluctuations in noise theory. Bell System Technical Journal, 53, 1041-1078.
230. Tikhonov, A. N. and Arsenin, V. A., (1977). Solution of Ill-Posed Problems, Winston & Sons, Washington.
231. Titchmarch, E. C. (1948). Introduction to the Theory of Fourier Integrals. Oxford, London.
232. Transistor Teacher's Summer School (1952). Experimental verification of the relation between diffusion constant and mobility of electrons and holes. Physical Review, 88, 1368-1369.
233. Tukey, J. W. (1961). Discussion, emphasising the connection between analysis of variance and spectral analysis. Technometrics, 3, 191-219; also in The Collected Works of John W. Tukey, ed. Brillinger, D. R., Wadsworth Advanced Books and Software, Belmont, California.
234. Tukey, J. W. (1968). An introduction to calculations of numerical spectral analysis. in Spectral Analysis of Time Series, ed. Harris, B., Wiley, New York, 25-46.
235. Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley, New York.
236. Turchin, V. F., Koslov, V. P., and Malkevich, M. S. (1971). The use of mathematicalstatistics methods in the solution of of incorrectly posed problems. Soviet Physics USPEKHI, 13, 681-840
237. Twomey, S. (1963). On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature. Journal of Association for Computing Machinary, 10, 97-101.
238. Uhlenbeck, G. E. and Ornstein, L. S. (1930). On the theory of Brownian motion. Physical Review, 36, 823-841.
239. Uspensky, J. V. (1937). Introduction to Mathematical Probability. McGraw-Hill, New York.
240. Valley, G. E. Jr. and Wallman, H. (1948). Vacuum Tube Amplifiers. MIT Radiation Lab Series, 13, McGraw-Hill, New York.
241. Wang, L. and Jacques, S. L. (1994). Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission. Physics in Medicine and Biology, 39, 2349.
242. Wang, M. C. and Uhlenbeck, G. E. (1945). On the theory of Brownian motion II. Reviews of Modern Physics, 17, 323-342.
243. Wannier, G. (1937). The structure of electronic excitation levels in insulating crystals. Physical Review, 52, 191.
244. Wax, N. (1954). Noise and Stochastic Processes. Dover, New York.
245. Welsh, D. (1988). Codes and Cryptography. Clarendon Press, Oxford, 41.
246. Welton, T. A. (1948). Some observable effects of the quantum-mechnical fluctuations of the electromagnetic field. Physical Review, 74, 1157.
247. Wiener, N. (1926). Harmonic analysis of irregular motion, Journal of Mathematical Physics, 5, 99.
248. Wiener, N. (1930). Generalized harmonic analysis. Acta Mathematica, 55, 117-258.
249. Wiener, N. (1949a). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Wiley, New York, and MIT Press, Cambridge.
250. Wiener, N. (1949b). Time Series. MIT Press, Cambridge.
251. Wigner, E. (1932). Quantum corrections for thermodynamic equilibrium. Physical Review, 40, 749-760.
252. Williams E. C. (1937). Thermal fluctuations in complex networks. Journal of Electrical Engineering, 81, 751.
253. Williams, E. C. (1936). Fluctuation voltage in diodes and in multi-electrode valves. Journal of the Institution of Electrical Engineers, 79, 349-360.
254. Williams, G. P. (1997). Chaos Theory Tamed. Joseph Henry Press, Washington.
255. Williams, N. H. and Vincent, H. B. (1926). Determination of electronic charge from measurements of shot-effect in aperiodic circuits. Physical Review, 28, 1250-1264.
256. Williams, N. H. and Huxford, W. S. (1929). Determination of Charge of positive thermions from measurements of shot effect. Physical Review, 33, 773-778.
257. Wold, H. O. A. (1938). A Study in the Analysis of Stationary Time Series. Almquist and Wiksell, Uppsala.
258. Wolf, P. E. and Maret, G. (1985). Weak localization and coherent backscattering of photons in disordered media. Physical Review Letters, 55, 2696-2699.
259. Xu, M., Cai, W., and Alfano, R. R. (2002). Photon migration in turbid media using a cumulant approximation to radiative transfer. Physical Review E, 65, 066609.
260. Xu, M., Cai, W., and Alfano, R. R. (2004). Multiple passages of light through an absorption inhomogeneity in optical imaging of turbid media. Optical Letters, 29, 1757-1759.
261. Xu, M., Cai, W., Lax, M., and Alfano, R. R. (2004). Stochastic view of photon migration in turbid media. arXiv.cond-mat, 0401409.
262. Xu, M. and Alfano, R. R. (2005). Random walk of polarized light in turbid media. Physical Review Letters, 95, 213905.
263. Xu, M. and Alfano, R. R. (2005). Circular polarization memory of light. Physical Review E, 72, 065601.
264. Yodh, A. G., Tromberg, B., Sevick-Muraca, E., and Pine, D. (1997). Diffusing photons in turbid media. Journal of the Optical Society of America A, 14, 136-342.