×

Estimations de grandes déviations pour les processus de diffusion a paramètre multidimensionnel. (Estimations of large deviations for diffusion processes with a multidimensional parameter). (French) Zbl 0604.60027

Probabilités XX, Proc. Sémin., Strasbourg 1984/85, Lect. Notes Math. 1204, 68-80 (1986).
[For the entire collection see Zbl 0593.00014.]
In this paper, estimations of the type of Ventcel and Freidlin are considered in the context of multiparameter processes. Large deviations estimations are first proved for multiparameter Brownian motion as a consequence of corresponding results for Gaussian measures on a separable Banach space. This result is then extended to the solutions of stochastic differential equations with respect to Brownian motion, using an exponential inequality for multiparameter strong martingales. Finally, the large deviations principle is applied to the asymptotic behaviour of the solution of the infinite-dimensional heat equation.

MSC:

60F10 Large deviations
60H20 Stochastic integral equations
60J60 Diffusion processes

Citations:

Zbl 0593.00014
Full Text: Numdam EuDML