On Markov–Kolmogorov principle for stochastic differential equations

For stochastic functions $\xi$ described by the partial differential equations (1) in $T\subseteq R^d$ the following principle is considered: for every domain $S\subseteq T$ there exists a «state» $\xi_\Gamma$ defined by corresponding values on boundary $\Gamma=\partial S$ such that for a given $\xi_\Gamma$ one has an unique solution of (1) in $S$ and moreover a behaviour of $\xi$ in $S$ is conditionally independent on its behaviour outside of $S$.