Large deviations and a Kramers' type law for self-stabilizing diffusions

Annals of Applied Probability

Volumn 18, Issue 4, 2008, Pages 1379-1423

  Herrmann, Samuel ^a   Imkeller, Peter ^b   Peithmann, Dierk ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Diffusion; Domain of attraction; Exit law; Exit time; Interacting particle systems; Large deviations; Propagation of chaos; Self stabilization

Indexed keywords

EID: 52949093541     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/07-AAP489     Document Type: Article

References (17)

1. BENACHOUR, S., ROYNETTE, B., TALAY, D. and VALLOIS, P. (1998). Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos. Stochastic Process. Appl. 75 173-201. MR1632193
2. BENACHOUR, S., ROYNETTE, B. and VALLOIS, P. (1998). Nonlinear self-stabilizing processes. II. Convergence to invariant probability. Stochastic Process. Appl. 75 203-224. MR1632197
3. GUILLIN, A., BOLLEY, F. and VILLANI, C. (2008). Quantitative concentration inequalities for empirical measures on non-compact spaces. Probab. Theory Related Fields 137 541-593. MR2280433
4. DAWSON, D. A. and GÄRTNER, J. (1987). Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics 20 247-308. MR0885876
5. DAY, M. V. (1983). On the exponential exit law in the small parameter exit problem. Stochastics 8 297-323. MR0693886
6. DAY, M. V. (1987). Recent progress on the small parameter exit problem. Stochastics 20 121-150. MR0877726
7. DEMBO, A. and ZEITOUNI, O. (1998). Large Deviations Techniques and Applications, 2nd ed. Springer, New York. MR1619036
8. FREIDLIN, M. and WENTZELL, A. (1998). Random Perturbations of Dynamical Systems, 2nd ed. Springer, New York. MR1652127
9. FUNAKI, T. (1984). A certain class of diffusion processes associated with nonlinear parabolic equations. Z Wahrsch. Verw. Gebiete 67 331-348. MR0762085
10. MALRIEU, F. (2001). Logarithmic Sobolev inequalities for some nonlinear PDE's. Stochastic Process. Appl. 95 109-132. MR1847094
11. MCKEAN, H. P., Jr. (1966). A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. U.S.A. 56 1907-1911. MR0221595
12. OELSCHLÄGER, K. (1985). A law of large numbers for moderately interacting diffusion processes. Z Wahrsch. Verw. Gebiete 69 279-322. MR0779460
13. STROOCK, D. W. and VARADHAN, S. R. S. (1979). Multidimensional Diffusion Processes. Springer, Berlin. MR0532498
14. SZNITMAN, A.-S. (1991). Topics in propagation of chaos. École d'Été de Prohabilités de Saint-Flour XIX - 1989. Lecture Notes in Math. 1464 165-251. Springer, Berlin. MRI108185
15. TAMURA, Y. (1984). On asymptotic behaviors of the solution of a nonlinear diffusion equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 195-221. MR0743525
16. TAMURA, Y. (1987). Free energy and the convergence of distributions of diffusion processes of McKean type. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 443-484. MR0914029
17. WILLIAMS, M. (1982). Asymptotic exit time distributions. SIAM J. Appl. Math. 42 149-154. MR0646755