Equivalence of the fractional Fokker-Planck and subordinated langevin equations: The case of a time-dependent force

Physical Review Letters

Volumn 101, Issue 21, 2008, Pages

  Magdziarz, Marcin ^a   Weron, Aleksander ^a   Klafter, Joseph ^b,c  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b TEL AVIV UNIVERSITY   (Israel)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FOKKER PLANCK EQUATION; MONTE CARLO METHODS; PHASE TRANSITIONS; RECONNAISSANCE AIRCRAFT;

FORCE FIELDS; FRACTIONAL FOKKER-PLANCK EQUATIONS; LANGEVIN; LANGEVIN EQUATIONS; LANGEVIN PROCESSES; PROBABILITY DENSITIES; SIMULATED TRAJECTORIES; SUBDIFFUSION;

PROBABILITY DENSITY FUNCTION;

EID: 56849094437     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.101.210601     Document Type: Article

References (28)

1. A. Einstein, Ann. Phys. (Leipzig) ANPYA2 0003-3804 17, 549 (1905).
2. P. Langevin, C.R. Seances Acad. Sci. COREAF 0001-4036 146, 530 (1908).
3. M. Smoluchowski, Phys. Z. PHZTAO 0369-982X 17, 557 (1916);
4. M. Smoluchowski Oeuvres de M. Smoluchowski, edited by, W. Natanson, (PAU, Krakow, 1924-1928).
5. M. Kac, Integration in Function Spaces and Some of Its Applications (Lezioni Fermiane, Pisa, 1980).
6. W. Ebeling and I.M. Sokolov, Statistical Thermodynamics and Nonequilibrium Systems (World Scientific, Singapore, 2005).
7. W.T. Coffey, Yu.P. Kalmykov, and J.T. Waldron, The Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering (World Scientific, Singapore, 2004).
8. K. Itô, Japan. J. Math. JJMAAK 0075-3432 18, 261 (1942).
9. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3
10. H. Scher, G. Margolin, R. Metzler, and J. Klafter, Geophys. Res. Lett. 29, 1061 (2002). GPRLAJ 0094-8276 10.1029/2001GL014123
11. I. Golding and E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.098102
12. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 61, 132 (2000). PLEEE8 1063-651X 10.1103/PhysRevE.61.132
13. I.M. Sokolov and J. Klafter, Phys. Rev. Lett. 97, 140602 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.140602
14. E. Heinsalu, M. Patriarca, I. Goychuk, and P. Hänggi, Phys. Rev. Lett. 99, 120602 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.120602
15. A. Weron, M. Magdziarz, and K. Weron, Phys. Rev. E 77, 036704 (2008). PLEEE8 1063-651X 10.1103/PhysRevE.77.036704
16. E. Barkai, Phys. Rev. E 63, 046118 (2001). PLEEE8 1063-651X 10.1103/PhysRevE.63.046118
17. S.G. Samko, A.A. Kilbas, and D.I. Maritchev, Integrals and Derivatives of the Fractional Order and Some of Their Applications (Gordon and Breach Science Publishers, Amsterdam, 1993).
18. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E 75, 016708 (2007). PLEEE8 1063-651X 10.1103/PhysRevE.75.016708
19. M.M. Meerschaert, D.A. Benson, H.P. Scheffler, and B. Baeumer, Phys. Rev. E 65, 041103 (2002). PLEEE8 1063-651X 10.1103/PhysRevE.65.041103
20. S. Eule, R. Friedrich, F. Jenko, and D. Kleinhans, J. Phys. Chem. B 111, 11474 (2007). JPCBFK 1520-6106 10.1021/jp072173h
21. A. Jurlewicz, K. Weron, and M. Teuerle, Phys. Rev. E 78, 011103 (2008). PLEEE8 1063-651X 10.1103/PhysRevE.78.011103
22. A. Piryatinska, A.I. Saichev, and W.A. Woyczynski, Physica (Amsterdam) 349A, 375 (2005). PHYADX 0378-4371 10.1016/j.physa.2004.11.003
23. M. Magdziarz and K. Weron, Physica (Amsterdam) 367A, 1 (2006). PHYADX 0378-4371 10.1016/j.physa.2005.12.011
24. A. Janicki and A. Weron, Simulation and Chaotic Behaviour of α-Stable Stochastic Processes (Marcel Dekker, New York, 1994).
25. I. Eliazar, and J. Klafter, Physica (Amsterdam) 336A, 219 (2004). PHYADX 0378-4371 10.1016/j.physa.2003.12.032
26. T. Koren, A.V. Chechkin, and J. Klafter, Physica (Amsterdam) 379A, 10 (2007). PHYADX 0378-4371 10.1016/j.physa.2006.12.039
27. D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes (Springer, New York, 2003).
28. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1971), Vol. 2, 2nd ed.