We show a method of uniform approximation of the value functions of uniformly nondegenerate stochastic differential games in smooth domains up to a constant over K with the ones having second-order derivatives bounded by a constant times K for any K≥1.

We prove the dynamic programming principle for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order “coefficient” and the “free” term are only assumed to be...

We extend several known results on solvability in the Sobolev spaces , p[set membership, variant][2,[infinity]), of SPDEs in divergence form in to equations having coefficients which are discontinuous in the space variable.

We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional...