Lévy processes and Schrödinger equation

Physica A: Statistical Mechanics and its Applications

Volumn 388, Issue 6, 2009, Pages 824-836

  Cufaro Petroni, Nicola ^a   Pusterla, Modesto ^b  

^a UNIVERSITY OF BARI   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

L vy processes; Schr dinger equation; Stochastic mechanics

Indexed keywords

KINETICS; MATHEMATICAL OPERATORS; STOCHASTIC SYSTEMS;

DIFFERENTIAL FORMS; DINGER EQUATION; INFINITELY DIVISIBLE LAWS; KINETIC-ENERGY OPERATOR; LAPLACIANS; NON-STABLE; PSEUDO-DIFFERENTIAL OPERATOR; STOCHASTIC MECHANICS;

KINETIC ENERGY;

EID: 58149336760     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2008.11.035     Document Type: Article

References (52)

1. Feynman R.P., and Hibbs A.R. Quantum Mechanics and Path Integrals (1965), McGraw-Hill, New York
2. Schulman L.S. Techniques and Applications of Path Integration (1981), Wiley, New York
3. Bohm D., and Vigier J.-P. Phys. Rev. 96 (1954) 208
4. Cufaro Petroni N., and Guerra F. Found. Phys. 25 (1995) 297
5. Fényes I. Z. Physik. 132 (1952) 81
6. Nelson E. Dynamical Theories of Brownian Motion (1967), Princeton, UP, Princeton
7. Nelson E. Quantum Fluctuations (1985), Princeton, UP, Princeton
8. Guerra F. Phys. Rep. 77 (1981) 263
9. Guerra F., and Morato L. Phys. Rev. D 27 (1983) 1774
10. Cufaro Petroni N., and Morato L. J. Phys. A 33 (2000) 5833
11. Albeverio S., Blanchard Ph., and Høgh-Krohn R. Expo. Math. 4 (1983) 365
12. Cufaro Petroni N., De Martino S., De Siena S., and Illuminati F. Phys. Rev. E 63 (2000) 016501
13. Cufaro Petroni N., De Martino S., De Siena S., and Illuminati F. Phys. Rev. ST. Accel. Beams. 6 (2003) 034206
14. Cufaro Petroni N., De Martino S., De Siena S., and Illuminati F. Phys. Rev. E 72 (2005) 066502
15. Cufaro Petroni N., De Martino S., De Siena S., and Illuminati F. Nucl. Instr. Meth. A 561 (2006) 237
16. Paul W., and Baschnagel J. Stochastic Processes: From Physics to Finance (1999), Springer, Berlin
17. Sato K. Lévy Processes and Infinitely Divisible Distributions (1999), Cambridge, UP, Cambridge
18. Protter Ph.E. Stochastic Integration and Differential Equations (2005), Springer, Berlin
19. Cont R., and Tankov P. Financial Modelling With Jump Processes (2004), Chapman&Hall/CRC, Boca Raton
20. Applebaum D. Lévy Processes and Stochastic Calculus (2004), Cambridge, UP, Cambridge
21. In: Barndorff-Nielsen O.E. (Ed). Lévy processes, Theory and applications (2001), Birkhäuser, Boston
22. Lévy P., et al. Théorie de l'addition des Variables Alatoires (1954), Gauthier-Villars, Paris
23. Lévy P. Processus Stochastiques et Mouvement Brownien (1965), Gauthier-Villars, Paris
24. Gnedenko B.V., and Kolmogorov A.N. Limit Distributions for Sums of Independent Random Variables (1968), Addison-Wesley
25. Loève M. Probability Theory I-II (1977-1978), Springer, Berlin
26. Bouchaud J.-., and Potters M. Theory of Financial Risks: From Statistical Physics to Risk Management (2000), Cambridge, UP, Cambridge
27. Mantegna R., and Stanley H.E. An Introduction to Econophysics (2001), Cambridge, UP, Cambridge
28. Metzler R., and Klafter J. Phys. Rep. 339 (2000) 1
29. Gorenflo R., and Mainardi F. Frac. Calc. Appl. Anal. 1 (1998) 167. http://www.fracalmo.org/) Reprinted at http://www.fracalmo.org/)
30. Gorenflo R., and Mainardi F. Arch. Mech. 50 (1998) 377. http://www.fracalmo.org/ Reprinted at http://www.fracalmo.org/
31. Laskin N. Phys. Rev. E 62 (2000) 3135
32. Laskin N. Phys. Rev. E 66 (2002) 056108
33. De Angelis G.F. J. Math. Phys. 31 (1990) 1408
34. Blanchard Ph., and Garbaczewski P. Phys. Rev. E 49 (1994) 3815
35. Garbaczewski P., Klauder J.R., and Olkiewicz R. Phys. Rev. E 51 (1995) 4114
36. Garbaczewski P., and Olkiewicz R. Phys. Rev. A 51 (1995) 3445
37. Garbaczewski P., and Olkiewicz R. J. Math. Phys. 40 (1999) 1057
38. Garbaczewski P., and Olkiewicz R. J. Math. Phys. 41 (2000) 6843
39. Risken H. The Fokker-Planck Equation (1996), Springer, Berlin
40. Gardiner C.W. Handbook of Stochastic Methods (1997), Springer, Berlin
41. Madelung E. Z. Physik 40 (1926) 332
42. Cufaro Petroni N. Physica A 387 (2008) 1894
43. Taylor M.E. Partial Differential Equations, Vol I-III (1996), Springer, Berlin
44. Jacob N. Pseudo-differential Operators and Markov Processes, Vol I-III (2001-05), Imperial College Press, London
45. Heyde C.C., and Leonenko N.N. Adv. Appl. Prob. 37 (2005) 342
46. Cufaro Petroni N. J. Phys. A 40 (2007) 2227
47. C. Berg, C. Vignat, On some results of Cufaro Petroni about student t-processes, arXiv:0803.3198v1[math.PR]
48. Vivoli A., Benedetti C., and Turchetti G. Nucl. Instr. Meth. A 561 (2006) 320
49. Beghi A., Ferrante A., and Pavon M. Quant. Inform. Proc. 1 (2002) 183
50. M. Pavon, Quantum Schrödinger bridges, arXiv:quant-ph/0306052v1
51. Bjorken J.D., and Drell S.D. Relativistic Quantum Mechanics (1964), McGraw-Hill, New York
52. Schweber S.S. An Introduction to Relativistic Quantum Field Theory (1961), Row, Peterson & Co., Evanston