Modeling scaled processes and 1/fβ noise using nonlinear stochastic differential equations

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2009, Issue 2, 2009, Pages

  Kaulakys, B ^a   Alaburda, M ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Current fluctuations; Stochastic processes; Stochastic processes (theory)

Indexed keywords

EID: 65449179946     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2009/02/P02051     Document Type: Article

References (146)

1. Johnson J B 1925 Phys. Rev. 26 71
2. Schottky W 1926 Phys. Rev. 28 74
3. Mandelbrot B B 1963 J. Bus. 36 394
4. Allan D W 1966 Proc. IEEE 54 221
5. Granger C W J 1966 Econometrica 34 150
6. Beran J 1994 Statistics for Long-Memory Processes (New York: Chapman and Hall)
7. Mandelbrot B B 1997 Fractals and Scaling in Finance (New York: Springer)
8. Mandelbrot B B 1999 Multifractals and 1/f Noise: Wild Self-Affinity in Physics (New York: Springer)
9. Mantegna R N and Stanley H E 2000 An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge: Cambridge University Press)
10. Racher S T (ed) 2003 Handbook of Heavy Tailed Distributions in Finance (Amsterdam: Elsevier)
11. Voss R F and Clarke J 1975 Nature 258 317
12. Press V H 1978 Comments Astrophys. 7 103
13. Gardner M 1978 Sci. Am. 238 16
14. Newman M E J 2005 Contemp. Phys. 46 323
15. Hooge F N, Kleinpenning T G M and Vadamme L K J 1981 Rep. Prog. Phys. 44 479
16. Dutta P and Horn P M 1981 Rev. Mod. Phys. 53 497
17. Kogan S M 1985 Usp. Fiz. Nauk. 145 285
18. Kogan S M 1985 Sov. Phys. Usp. 28 170 (translation)
19. Weissman M B 1988 Rev. Mod. Phys. 60 537
20. Van Vliet C M 1991 Solid-State Electron. 34 1
21. Zhigalskii G P 1997 Usp. Fiz. Nauk. 167 623
22. Zhigalskii G P 1997 Sov. Phys. Usp. 40 599 (translation)
23. Zhigal'skii G P 2003 Usp. Fiz. Nauk. 56 449
24. Wong H 2003 Microelectron. Reliab. 43 585
25. Musha T and Higuchi H 1976 Japan. J. Appl. Phys. 15 1271
26. Lawrence A, Watson M G, Pounds K A and Elvis M 1987 Nature 325 695
27. Gilden D L, Thornton T and Mallon M W 1995 Science 267 1837
28. Gabaix X, Gopikrishnan P, Plerou V and Stanley E 2003 Nature 423 267
29. Carbone A, Kaniadakis G and Scarfone A M 2007 Eur. Phys. J. B 57 121
30. Smeets R M M, Keyser U F, Dekker N H and Dekker C 2008 Proc. Nat. Acad. Sci. 105 417
31. Kaulakys B and Meškauskas T 1998 Phys. Rev. E 58 7013
32. Kaulakys B 1999 Phys. Lett. A 257 37
33. Kaulakys B, Gontis V and Alaburda M 2005 Phys. Rev. E 71 051105
34. Li W 2009 http://www.nslij-genetics.org/wli/1fnoise
35. Milotti E 2002 arXiv:physics/0204033
36. Li W 2007 http://www.nslij-genetics.org/wli/1fnoise/index-by-category. html
37. Scholarpedia 2009 http://www.scholarpedia.org/article/1/f-noise
38. Mandelbrot B B and Van Ness J W 1968 SIAM Rev. 10 422
39. Masry E 1991 IEEE Trans. Inform. Theory 37 1173
40. Milotti E 1995 Phys. Rev. E 51 3087
41. Mamontov Y V and Willander M 1997 Nonlinear Dyn. 12 399
42. Ninness B 1998 IEEE Trans. Inform. Theory 44 32
43. Jumarie G 2005 Appl. Math. Lett. 18 739
44. Milotti E 2005 Phys. Rev. E 72 056701
45. Ostry D I 2006 IEEE Trans. Inform. Theory 52 1609
46. Erland S and Greenwood P E 2007 Phys. Rev. E 76 031114
47. Bernamont J 1937 Ann. Phys. 7 71
48. Surdin M 1939 J. Phys. Radium 10 188
49. Van der Ziel A 1950 Physica (Amsterdam) 16 359
50. McWhorter A L 1957 Semiconductor Surface Physics ed R H Kingston (Philadelphia, PA: University of Pennsylvania) p207
51. Ralls K S, Skocpol W J, Jackel L D, Howard R E, Fetter L A, Epworth R W and Tennant D M 1984 Phys. Rev. Lett. 52 228
52. Rogers C T and Buhrman R A 1984 Phys. Rev. Lett. 53 1272
53. Palenskis V 1990 Litov. Fiz. Sb. 30 107
54. Palenskis V 1990 Lith. Phys. J. 30 (2) 1
55. Watanabe S 2005 J. Korean Phys. Soc. 46 646
56. Kaulakys B, Alaburda M and Ruseckas J 2007 AIP Conf. Proc. 922 439
57. Palenskis V and Shoblitskas Z 1982 Solid State Commun. 43 761
58. Kogan S M and Nagaev K E 1984 Solid State Commun. 49 387
59. Shtengel K and Yu C C 2003 Phys. Rev. B 67 165106
60. Burin A L, Shklowskii B I, Kozub V I, Galperin Y M and Vinokur V 2006 Phys. Rev. B 74 075205
61. Muller J, von Molnar S, Ohno Y and Ohno H 2006 Phys. Rev. Lett. 96 186601
62. Koch R H, DiVincento D P and Clarke J 2007 Phys. Rev. Lett. 98 267003
63. de Sousa R 2007 Phys. Rev. B 76 245306
64. Burin A L, Shklowskii B I, Kozub V I, Galperin Y M and Vinokur V 2008 Phys. Status Solidi c 5 800
65. D'Souza A I, Stapelbroek M G, Robinson E W, Yoneyama C, Mills H A, Kinch M A, Skokan M R and Shih H D 2008 J. Electron. Mater. 37 1318
66. Handel P H 1975 Phys. Rev. Lett. 34 1492
67. Handel P H 1975 Phys. Rev. Lett. 34 1495
68. Kazakov K A 2008 Physica B 403 2255
69. Foster S 2008 Phys. Rev. A 78 013820
70. Relano A, Gomez J M G, Molina R A, Retamosa J and Faleiro E 2002 Phys. Rev. Lett. 98 244102
71. Salasnich L 2005 Phys. Rev. E 71 047202
72. Abul-Magd A Y, Dietz B, Friedrich T and Richter A 2008 Phys. Rev. E 77 046202
73. Bak P, Tang C and Wiesenfeld K 1987 Phys. Rev. Lett. 59 381
74. Bak P, Tang C and Wiesenfeld K 1988 Phys. Rev. A 38 364
75. Jensen H J, Christensen K and Fogedby H C 1989 Phys. Rev. B 40 7425
76. Takayasu H 1989 Phys. Rev. Lett. 63 2563
77. Kertesz J and Kiss L B 1990 J. Phys. A: Math. Gen. 23 L433
78. Jaeger H M and Nagel S R 1992 Science 255 1523
79. Paczuski M, Maslov S and Bak P 1996 Phys. Rev. E 53 414
80. Davidsen J and Schuster H G 2000 Phys. Rev. E 62 6111
81. Laurson L, Alava M J and Zapperi S 2005 J. Stat. Mech. L11001
82. Laurson L and Alava M J 2006 Phys. Rev. E 74 066106
83. Poil S S, van Ooyen A and Linkenkaer-Hansen K 2008 Hum. Brain Mapping 29 770
84. Kuntz M C and Sethna J P 2000 Phys. Rev. B 62 11699
85. Heiden C 1969 Phys. Rev. 188 319
86. Schick K L and Verveen A A 1974 Nature 251 599
87. Ruseckas J, Kaulakys B and Alaburda M 2003 Lith. J. Phys. 43 223 [arXiv:0812.4674]
88. Kaulakys B, Alaburda M, Gontis V, Meškauskas T and Ruseckas J 2007 Traffic and Granular Flow'05 ed A Schadschneider, T Poschel, R Kuhne, M Schreckenberg and D E Wolf (Berlin: Springer) p603 [arXiv:physics/0512068]
89. Frigg R 2003 Stud. Hist. Phil. Sci. 34 613
90. Dhar D 2006 Physica A 369 29
91. Baiesi M and Maes C 2006 Europhys. Lett. 75 413
92. Davidsen J and Paczuski M 2002 Phys. Rev. E 66 050101(R)
93. Bunde A, Eichner J F, Havlin S and Kantelhardt J W 2004 Physica A 342 308
94. Bunde A, Eichner J F, Kantelhardt J W and Havlin S 2005 Phys. Rev. Lett. 94 048701
95. Eichner J F, Kantelhardt J W, Bunde A and Havlin S 2007 Phys. Rev. E 75 011128
96. Blender R, Fraedrich K and Sienz F 2008 Nonlin. Processes Geophys. 15 557
97. Sethna J P, Dahmen K A and Myers C R 2001 Nature 410 242
98. Eggenhoffner R, Celasco E and Celasco M 2007 Fluct. Noise Lett. 7 L351
99. Cote P J and Meisel L V 1991 Phys. Rev. Lett. 67 1334
100. Meisel L V and Cote P J 1992 Phys. Rev. B 46 10822
101. Colaiori F 2008 Adv. Phys. 57 287
102. Telesca L, Cuomo V, Lapenna V and Macchiato M 2002 Fluct. Noise Lett. 2 L357
103. Davidsen J, Grassberger P and Paczuski M 2008 Phys. Rev. E 77 066104
104. Novak U and Usadel K D 1991 Phys. Rev. B 43 851
105. Koverda V P, Skokov V N and Skripov V P 1998 J. Exp. Theor. Phys. 86 953
106. Fukuda K, Takayasu H and Takayasu M 2000 Physica A 287 289
107. Koverda V P and Skokov V N 2005 Physica A 346 203
108. Kaulakys B and Meškauskas T 1999 Nonlinear Anal.: Model. Control 4 87
109. Kaulakys B and Meškauskas T 2000 Microelecron. Reliab. 40 1781
110. Kaulakys B 2000 Microelecron. Reliab. 40 1787
111. Kaulakys B 2000 Lith. J. Phys. 40 281
112. Gontis V and Kaulakys B 2004 Physica A 343 505
113. Gontis V and Kaulakys B 2004 Physica A 344 128
114. Gontis V and Kaulakys B 2006 J. Stat. Mech. P10016
115. Gontis V and Kaulakys B 2007 Physica A 382 114
116. Gontis V, Kaulakys B and Ruseckas J 2008 Physica A 387 3891
117. Kaulakys B and Ruseckas J 2004 Phys. Rev. E 70 020101(R)
118. Kaulakys B, Ruseckas J, Gontis V and Alaburda M 2006 Physica A 365 217
119. Thurner S, Lowen S B, Feurstein M C, Heneghan C, Feichtinger H G and Teich M C 1997 Fractals 5 565
120. Schwalger T and Schimansky-Geier L 2008 Phys. Rev. E 77 031914
121. Perello J, Masoliver J, Kasprzak A and Kutner R 2008 Phys. Rev. E 78 036108
122. Arnold P 2000 Phys. Rev. E 61 6091
123. Kupferman R, Pavliotis G A and Stuart A M 2004 Phys. Rev. E 70 036120
124. Theiler J 1991 Phys. Lett. A 155 480
125. Talocia S G 1995 Phys. Lett. A 200 264
126. Caprari R S 1998 J. Phys. A: Math. Gen. 31 3205
127. Kaulakys B, Alaburda M, Gontis V and Meškauskas T 2006 Conplexus Mundi: Emergent Patterns in Nature ed M M Novak (Singapore: World Scientific) p277
128. Barabasi A L and Stanley H E 1995 Fractal Concepts in Surface Growth (Cambridge: Cambridge University Press)
129. Yang H-N and Lu T-M 1995 Phys. Rev. B 51 2479
130. Zhao Y-P, Cheng C-F, Wang G-C and Lu T-M 1998 Surface Science 409 L703
131. Yanguas-Gil A, Cotrino J, Walkiewicz-Pietrzykowska A and Gonzalez-Elipe A R 2007 Phys. Rev. B 76 075314
132. Palasantzas G 2008 J. Appl. Phys. 104 053524
133. Timashev S F and Polyakov Y S 2007 Fluct. Noise Lett. 7 R15
134. Gruneis F 1984 Physica A 123 149
135. Gruneis F and Musha T 1986 Japan. J. Appl. Phys. 25 1504
136. Gruneis F 2001 Fluct. Noise Lett. 1 R119
137. Takayasu H and Takayasu M 2003 Physica A 324 101
138. Gontis V, Kaulakys B and Ruseckas J 2005 AIP Conf. Proc. 776 144
139. Gruneis F 2000 Physica A 282 108
140. Gruneis F 2000 Physica A 290 512 (Corrigendum)
141. Gruneis F 2007 Fluct. Noise Lett. 7 C1
142. Derksen H E and Verveen A A 1966 Science 151 1388
143. Bezrukov S M and Winterhalter M 2000 Phys. Rev. Lett. 85 202
144. Siwy Z and Fulinski A 2002 Phys. Rev. Lett. 89 158101
145. Banerjee J, Verma M K, Manna S and Ghosh S 2006 Europhys. Lett. 73 457
146. Kosinska I D and Fulinski A 2008 Europhys. Lett. 81 50006