Some remarks on the Smoluchowski-Kramers approximation

Journal of Statistical Physics

Volumn 117, Issue 3-4, 2004, Pages 617-634

  Freidlin, Mark ^a  

^a Bldg 142   (United States)

Author keywords

homogenization; large deviations; Smoluchowski Kramers approximation; stochastic resonance

Indexed keywords

EID: 7244229982     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-004-2273-9     Document Type: Article

References (19)

1. M. Smoluchowski, Drei Vortrage über Diffusion Brownsche Bewegung and Koagulation von Kolloidteilchen. Phys. Z. 17:557-585 (1916).
2. H. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284-304 (1940).
3. E. Nelson, Dynamical Theories of Brownian Motion. (Princeton University Press).
4. Z. Schuss, Theory and Applications of Stochastic Differential Equations. (Wiley, 1980).
5. C. W. Gardiner, Handbook of Stochastic Methods. (Springer, 1985).
6. P. Hänggi, P. Talkner, M. Borkovec, Reaction-rate theory: fifty years after Kramers. Rev. of Modern Phys. 62(2): 251-341 (1990).
7. P. Hänggi, P. Jung, F. Marchesoni, Stochastic resonance. Rev. of Modern Phys. 70(1): 223-287 (1998).
8. E. Wong and M. Zakai, On the convergence of ordinary integrals to stochastic intergrals. Ann. Math. Stat. 36:1560-1564 (1965).
9. M. I. Freidlin, On stable oscillations and equilibriums induced by small noise. J. Stat. Phy. 103:283-300 (2001).
10. M. I. Freidlin, On stochastic perturbations of dynamical system with fast and slow components. Stochastics and Dynamics 1:261-281 (2001).
11. M. Freidlin and A. Wentzell, Random Perturbations of Dynamical Systems, 2nd e. (Springer, 1998).
12. M. Freidlin and M. Weber, Random perturbations of nonlinear oscillators. Ann. Probab. 26:1-43 (1998).
13. H. Cramer and M. Leadbetter, Stationary and Related Stochastic processes (Wiley, 1967).
14. M. I. Freidlin, Dirichlet's problem for equations with periodic coefficients, Probab. Theory and Appl. 9:133-139 (1964).
15. A. Bensoussan, J. L. Lions, G. C. Papanicolaou, Asymptotic Analysis for Periodic Structures. North-Holland Publ. Co., (1978).
16. G. Papanicolaou and S. R. S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Proceedings of the conference on random fields, Esztergon, Hungary, Colloguia Math. Soc. Janos Bolyai 27:235-273 (1981).
17. K. Ito and H. Mckean, Diffusion processes and their sample paths (Springer, 1965).
18. M. Freidlin and A. Wentzell, Averaging Principle for stochastic perturbations of multi-frequency systems, Stochastics and Dynamics 3:393-408 (2003).
19. M. I. Freidlin, Quasi-deterministic approximation, metastability, and stochastic resonance. Physica D 137:333-352 (2000).