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arXiv · 1610.09687

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

Alexander Veretennikov
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Abstract

In earlier papers Poisson equation 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 diffusion approximation in the theory of stochastic averaging and homogenisation. Here a similar equation 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.

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Alexander Veretennikov. 2016-10-30. On Poisson equations with a potential in the whole space for "ergodic" generators. https://doi.org/10.1090/tpms%2F1029

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