Nonlinear self-stabilizing processes - I Existence, invariant probability, propagation of chaos

Stochastic Processes and their Applications

Volumn 75, Issue 2, 1998, Pages 173-201

  Benachour, S ^a   Roynette, B ^a   Talay, D ^b   Vallois, P ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

^b INRIA   (France)

Author keywords

60H10; 60J60; 60K35

Indexed keywords

EID: 0040687609     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(98)00018-0     Document Type: Article

References (10)

1. Dawson, D., 1983. Critical dynamics and fluctuations for a mean-field model of cooperative behavior. J. Statist. Phys. 31 (1), 29-85.
2. Funaki T. A certain class of diffusion processes associated with nonlinear parabolic equations. Z. Wahrscheinlichkeistheorie Verw. Gebiete. 67:1984;331-348.
3. Gilbarg, D., Trudinger, N.S., 1977. Elliptic Partial Differential Equations of Second Order, Gründlehren der Math. Wissenschaften., vol. 224. Springer, Berlin.
4. Mc Kean, 1966. A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. 56, 1907-1911.
5. Oelschläger K. A law of large numbers for moderately interacting diffusion process. Z. Warscheinlichkeitstheorie Verw. Gebiete. 69:1985;279-322.
6. Sznitman, A.S., 1989. Topics in propagation of chaos. In Ecole d'Eté de Saint Flour XIX. Lecture Notes in Math., vol. 1464. Springer, Berlin.
7. Stroock, D.W., Varadhan, S.R.S., 1979. Multidimensional diffusion process, Gründlehren der Math. Wissenschaften, vol. 233. Springer, Berlin.
8. Sznitman A.S, Varadhan S.R.S. A multidimensional process involving local time. Z. Wahrscheinlichk- eitstheor. Verw. Gebiete. 71:1986;553-579.
9. Tamura Y. On asymptotic behaviors of the solution of a non linear diffusion equation. J. Fac. Sciences Univ. Tokyo. Section IA Math. 31:1984;195-221.
10. Tamura Y. Free energy and the convergence of distribution of diffusion processes of McKean type. J. Fac. Sciences Univ. Tokyo. Section IA, Math. 34:1987;443-484.