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On large deviations of solutions of nonlinear stochastic equations. (Russian. English summary) Zbl 0675.60022

The large deviations principle is established for solutions of nonlinear partial stochastic differential equations \[ u(t,x)=\Delta_ xu(t,x)- f(u(t,x))+\epsilon w(t,x),\quad \epsilon \to 0. \] The result is a nontrivial analogue of the finite-dimensional theorems of A. D. Ventcel’ and M. I. Freídlin [Usp. Mat. Nauk 25, No.1(151), 3- 55 (1970; Zbl 0291.34042); English translation in Russ. Math. Surveys 25, No.1, 1-55 (1970)].
Reviewer: A.Yu.Veretennikov

MSC:

60F10 Large deviations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Citations:

Zbl 0291.34042
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