The exit problem for diffusions with time-periodic drift and stochastic resonance

Annals of Applied Probability

Volumn 15, Issue 1 A, 2005, Pages 39-68

  Herrmann, Samuel ^a,b   Imkeller, Peter ^a,c  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^c HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Comparison theorem; Diffusion; Double well potential; Exit time distribution; Low lying eigenvalue; Noise induced transition; Periodic potential; Perturbed dynamical system; Spectral theory; Stochastic resonance

Indexed keywords

EID: 14544295404     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/105051604000000530     Document Type: Article

References (19)

1. BENZI, R., PARISI, G., SUTERA, A. and VULPIANI, A. (1983). A theory of stochastic resonance in climatic change. SIAM J. Appl. Math. 43 565-578.
2. BERGLUND, N. and GENTZ, B. (2002). Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations. Stoch. Dyn. 2 327-358.
3. BOVIER, A., ECKHOFF, M., GAYRARD, V. and KLEIN, M. (2002). Metastability in reversible diffusion processes I. Sharp asymptotics for capacities and exit times. Unpublished manuscript.
4. BOVIER, A., GAYRARD, V. and KLEIN, M. (2002). Metastability in reversible diffusion processes II. Precise asymptotics for small eigenvalues. Unpublished manuscript.
5. DAY, M. V. (1983). On the exponential exit law in the small parameter exit problem. Stochastics 8 297-323.
6. DAY, M. V. (1987). Recent progress on the small parameter exit problem. Stochastics 20 121-150.
7. FREIDLIN, M. (2000). Quasi-deterministic approximation, metastability and stochastic resonance. Phys. D 137 333-352.
8. FREIDLIN, M. and WENTZELL, A. (1998). Random Perturbations of Dynamical Systems, 2nd ed. Springer, New York.
9. FREUND, J. A., NEIMAN, A. B. and SCHIMANSKY-GEIER, L. (2001). Stochastic resonance and noise-induced phase coherence. In Stochastic Climate Models (P. Imkeller and von J.-S. Storch, eds.) 309-323. Birkhäuser, Basel.
10. GAMMAITONI, L., HÄNGGI, P., JUNG, P. and MARCHESONI, F. (1998). Stochastic resonance. Rev. Mod. Phys. 70 223-287.
11. HERRMANN, S. and IMKELLER, P. (2002). Barrier crossings characterize stochastic resonance. Stoch. Dyn. 2 413-436.
12. IMKELLER, P. and PAVLYUKEVICH, I. (2001). Stochastic resonance in two-state Markov chains. Arch. Math. (Basel) 77 107-115.
13. IMKELLER, P. and PAVLYUKEVICH, I. (2002). Model reduction and stochastic resonance. Stoch. Dyn. 2 463-506.
14. KRAMERS, H. A. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Phys. VII 4 284-304.
15. MCNAMARA, B. and WIESENFELD, K. (1989). Theory of stochastic resonance. Phys. Rev. A 39 4854-4869.
16. MILSTEIN, G. M. and TRETJAKOV, M. V. (2000). Numerical analysis of noise-induced regular oscillations. Phys. D 140 244-256.
17. NICOLIS, C. (1982). Stochastic aspects of climatic transitions - responses to periodic forcing. Tellus 34 1-9.
18. PAVLYUKEVICH, I. (2002). Stochastic resonance. Ph.D. thesis, Humboldt-Univ. zu Berlin.
19. REVUZ, D. and YOR, M. (1999). Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin.