It is shown that value functions for controlled degenerate diffusion processes can be approximated with error of order $h^{1/3}$ by using policies which are constant on intervals $[kh^{2},(k+1)h^{2})$.

Genetic models incorporating resampling and migration are now fairly well-understood. Problems arise in the analysis, if both selection and mutation are incorporated. This paper addresses some aspects of this problem, in particular the analysis of the long-time behaviour before the…

In this paper we investigate stopped partial sums for weak dependent sequences. In particular, the results are used to obtain new maximal inequalities for strongly mixing sequences and related almost sure results.

We establish a large deviations type evaluation for the family of integral functionals.

In this paper a nonautonomous dynamical system is considered, a stochastic one that is obtained from the dissipative Euler equation subject to a stochastic perturbation, an additive noise. Absorbing sets have been defined as sets that depend on time and…

Following the Arnold-Marsden-Ebin approach, we prove local (global in 2-D) existence and uniqueness of classical (Hölder class) solutions of stochastic Euler equation with random forcing.

The intersection exponents for planar Brownian motion measure the exponential decay of probabilities of nonintersection of paths. We study the intersection exponent $\xi(\lambda_1,\lambda_2)$ for Brownian motion restricted to a half plane which by conformal invariance is the same as Brownian…

Two Chung-type and Hirsch-type laws are established to describe the liminf asymptotic behaviours of the Cauchy's principal values related to Brownian local times. These results are generalized to a class of Brownian additive functionals.

On the Wiener space $\Omega$, we introduce an abstract Ricci process $A_t$ and a pseudo-gradient $F\rightarrow{F}^\sharp$ which are compatible through an integration by parts formula. They give rise to a $\sharp$-Sobolev space on $\Omega$, logarithmic Sobolev inequalities, and capacities, which…

Existence and uniqueness theorems are presented for evolutional stochastic partial differential equations of second order in $L_p$-spaces with weights allowing derivatives of solutions to blow up near the boundary. It is allowed for the powers of summability with respect to…