The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control.

and Applied Analysis 3 with initial data x 0 x0, where f :R ×Rn → R, g:R ×Rn → Rn×d, x0 is a vector, and · denotes the greatest-integer function. By the definition of stochastic differential, this equation is equivalent to the following stochastic integral equation:

This thesis considers a stochastic dynamical system that has multiple time scales. The focus lies on the planar slow-fast stochastic differential equation (a singularly perturbed stochastic system) modeling the spiking activity of an isolated FitzHugh-Nagumo neural oscillator. We analyze the model equation on the slow time scale τ (Eq.(1)) and on the fast time scale t (Eq.(2)). { dvτ = ε f(vτ ,...

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some second order Hamilton-Jacobi equation. Key-words : stochastic differential game, asymmetric information, viscosity solution. A.M.S. classification : 49N70, 49L...

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

The purpose of this article is to giye an overview of some recent developments in optimal stochastic control theory. The field has expanded a great deal during the last 20 years. It is not possible in this overview to go deeply into any topic, and a number of interesting topics have been omitted entirely. The list of references includes several books, conference proceedings and survey articles....