Fractional Feynman-Kac Equation for Non-Brownian Functionals

Physical Review Letters

Volumn 103, Issue 19, 2009, Pages

  Turgeman, Lior ^a   Carmi, Shai ^a   Barkai, Eli ^a  

^a BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; ERGODICITY; FUNCTIONALS; HALF SPACES; NON-BROWNIAN;

EID: 70449850116     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.103.190201     Document Type: Article

References (25)

1. M. Kac, Trans. Am. Math. Soc. 65, 1 (1949); TAMTAM 0002-9947 10.2307/1990512
2. M. Kac, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, CA, 1951), p.189.
3. S.N. Majumdar, Curr. Sci. CUSCAM 0011-3891 89, 2076 (2005).
4. A.M. Obukhov, Adv. Geophys. ADGOAR 0065-2687 6, 113 (1959).
5. A. Baule and R. Friedrich, Phys. Lett. A 350, 167 (2006). PYLAAG 0375-9601 10.1016/j.physleta.2005.10.017
6. S. Havlin and D. ben-Avraham, Adv. Phys. ADPHAH 0001-8732 36, 695 (1987). 10.1080/00018738700101072
7. J.P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990). PRPLCM 0370-1573 10.1016/0370-1573(90)90099-N
8. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3
9. S.N. Majumdar and A. Comtet, Phys. Rev. Lett. 89, 060601 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.060601
10. E. Barkai, J. Stat. Phys. JSTPSB 0022-4715 123, 883 (2006). 10.1007/s10955-006-9109-8
11. H. Scher and E. Montroll, Phys. Rev. B PLRBAQ 0556-2805 12, 2455 (1975). 10.1103/PhysRevB.12.2455
12. R. Friedrich, F. Jenko, A. Baule, and S. Eule, Phys. Rev. Lett. 96, 230601 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.230601
13. E.W. Montroll and G.H. Weiss, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 6, 167 (1965). 10.1063/1.1704269
14. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E PLEEE8 1063-651X 61, 132 (2000). 10.1103/PhysRevE.61.132
15. J. Lamperti, Trans. Am. Math. Soc. 88, 380 (1958). TAMTAM 0002-9947 10.2307/1993222
16. R. Metzler, E. Barkai, and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 82, 3563 (1999). 10.1103/PhysRevLett.82.3563
17. S.N. Majumdar and A.J. Bray, Phys. Rev. E PLEEE8 1063-651X 65, 051112 (2002). 10.1103/PhysRevE.65.051112
18. M. Magdziarz, A. Weron, and K. Weron, Phys. Rev. E PLEEE8 1539-3755 75, 016708 (2007). 10.1103/PhysRevE.75.016708
19. D. Kleinhans and R. Friedrich, Phys. Rev. E PLEEE8 1539-3755 76, 061102 (2007). 10.1103/PhysRevE.76.061102
20. G. Bel and E. Barkai, Phys. Rev. Lett. 94, 240602 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.240602
21. A. Rebenshtok and E. Barkai, Phys. Rev. Lett. 99, 210601 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.210601
22. A. Rebenshtok E. Barkai J. Stat. Phys. JSTPSB 0022-4715 133, 565 (2008). 10.1007/s10955-008-9610-3
23. I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999).
24. N. Laskin, Phys. Rev. E PLEEE8 1063-651X 62, 3135 (2000). 10.1103/PhysRevE.62.3135
25. M. Naber, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 45, 3339 (2004). 10.1063/1.1769611