We prove the existence of martingale solutions and of stationary solutions of stochastic
Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary …

We consider a Burgers equation perturbed by a multiplicative white noise. We prove the
existence and uniqueness of the global solution as well as the strong Feller property and …

We give an existence theorem for an abstract nonlinear stochastic evolution equation in a
Hilbert space. The result is applicable to the stochastic Navier-Stokes equation in any …

In this paper we study the existence and uniqueness of weak solutions of stochastic differential
equations on Banach spaces. We also study the existence of invariant measures for the …

… We require the process W: to be a standard Wiener process under certain probability Pr*
absolutely continuous with respect to Pr, so by the Girsanov formula d W: = d Wt + {, dt for …

We consider nonlinear stochastic evolution equation in Hilbert space. A simple new proof of
existence of weak solution is given provided C 0 -semigroup governing the linear part of this …

… BRE Bank where he worked together with Dariusz Gatarek and he was engaged in quantitative
… Since most financial models are multidimensional we have chosen the less elegant d-…

… for arbitrary v E D(A*), t 2 0 … Since Yx(t) E D(A) for any t _> 0 and … Denote by L$(R x [O,T];
L(U; H)) the space of such L(U; H)-valued processes d(t) such that d(.)y E L$(R x (O,T]; H ) …

… for any w 9 D(A) and x 9 E. The domain of the generator D(A) is characterized in … Conversely,
ifv e D(A), then v is a generalized solution to (26)-(27) and there exists an optimal stopping …

An optimal control problem is studied for a Hilbert space-valued diffusion. Existence of an
optimal control in the class of relaxed controls is proved. As a tool, the factorization method …