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Theory of Probability and Mathematical Statistics



On Poisson equations with a potential in the whole space for "ergodic" generators

Alexander Veretennikov

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Abstract: In \cite{PV01, PV03, PV05, Ver11, KV11} Poisson equation \emph{in the whole space} was studied for so called ergodic generators $L$ corresponding to homogeneous Markov diffusions ($X_t, \, t\ge 0$) in $\mathbb R^d$. Solving this equation is one of the main tools for {\it diffusion approximation} in the theory of stochastic averaging and homogenisation. Here a similar equation {\it with a potential} is considered, firstly because it is natural for PDEs, and secondly with a hope that it may be also useful for some extensions related to homogenization and averaging.

Keywords: SDE, large deviations, Poisson equation, potential, exponential bounds

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