Exact solution to the exit-time problem for an undamped free particle driven by gaussian white noise

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 3, 1996, Pages 2243-2256

  Masoliver, Jaume ^a   Porrà, Josep M ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5244378809     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.2243     Document Type: Article

References (38)

1. G. H. Weiss, J. Stat. Phys.42, 3 (1986), and references therein.
2. P. Hanggi, P. Talkner and M. Borkovec, Rev. Mod. Phys.62, 251 (1990), and references therein.
3. V. I. Melnikov, Phys. Rep.209, 1 (1991), and references therein.
4. S. O. Rice, in Noise and Stochastic Processes, edited by N. Wax (Dover, New York, 1954); D. Middleton, An Introduction to Statistical Communication Theory (Academic, New York, 1960).
5. S. H. Crandall and W. D. Mark, Random Vibrations in Dynamical Systems (Academic, New York, 1963); J. B. Roberts, in Stochastic Problems in Dynamics, edited by B. L. Clarkson (Pitman, London, 1977).
6. H. A. Kramers, Physica7, 284 (1940).
7. K. Lindenberg and B. J. West, J. Stat. Phys.42, 201 (1986), and references therein.
8. Z. Schuss, Theory and Applications of Stochastic Differential Equations (Wiley, New York, 1980); C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer Verlag, Berlin, 1990).
9. D. A. Darling and A. J. F. Siegert, Am. Math Stat. 24, 624 (1953);
10. G. H. Weiss, Adv. Chem. Phys.13, 1 (1966).
11. J. Masoliver and J. M. Porrà, Phys. Rev. Lett.75, 189 (1995).
12. G. Fichera, in Boundary Problems in Differential Equations, edited by R. E. Langer (The University of Wisconsin Press, Madison, 1960);
13. O. A. Oleinik, Sov. Math.5, 1129 (1964);
14. J. N. Yang and M. Shinozuka, J. Acoust. Soc. Am.47, 393 (1970).
15. M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys.17, 323 (1945).
16. T. W. Marshall and E. J. Watson, J. Phys. A18, 3531 (1985);
17. T. W. Marshall and E. J. Watson, J. Phys. A20, 1345 (1987).
18. M. A. Burschka and U. M. Titulaer, J. Stat. Phys.25, 569 (1981);
19. M. A. Burschka and U. M. Titulaer, Physica112A, 315 (1982)
20. P. W. Duck, T. W. Marshall and E. J. Watson, J. Phys. A19, 3545 (1986);
21. A. J. Kainz and U. M. Titulaer, J. Phys. A24, 4677 (1991).
22. H. P. McKean, J. Math. Kyoto Univ.2, 227 (1963);
23. M. Goldman, Am. Math. Stat.42, 2150 (1971);
24. M. Lefebre, SIAM J. Appl. Math.49, 1514 (1989).
25. T. Maeh, M. M. Klosek, B. J. Matkowski and Z. Schuss, SIAM J. Appl. Math.50, 595 (1990), and references therein.
26. W. R. LePage, Complex Variables and the Laplace Transform for Engineers (Dover, New York, 1980).
27. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965).
28. G. E. Roberts and H. Kaufman, Table of Laplace Transforms (Saunders, Philadelphia, 1966).
29. J. M. Porrà, J. Masoliver and K. Lindenberg, Phys. Rev E50, 1985 (1994).
30. W. Horsthemke and R. Lefever, Noise Induced Transitions (Springer, Berlin, 1984).
31. A. J. Bray and A. J. McKane, Phys. Rev. Lett.62, 493 (1989).
32. R. S. Maier and D. L. Stein, Phys. Rev. Lett.71, 1783 (1993);
33. R. S. Maier and D. L. Stein, Phys. Rev. E48, 931 (1993).
34. J. Masoliver, Phys. Rev. A45, 706 (1992);
35. J. Masoliver, Phys. Rev. E48, 121 (1993).
36. I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).
37. D. Porter and D. S. G. Stirling, Integral Equations (Cambridge University Press, Cambridge, 1990).
38. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series (Gordon and Breach, New York, 1990), Vol. III.