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Theory of Probability and Mathematical Statistics

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

Author: Alexander Veretennikov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 95 (2016).
Journal: Theor. Probability and Math. Statist. 95 (2017), 195-206
Published electronically: February 28, 2018
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Abstract: In earlier works 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 $ \mathbf {R}^d$. Solving this equation is one of the main tools for diffusion approximation in the theory of stochastic averaging and homogenization. Here a similar equation with a potential is considered, first because it is natural for PDEs, and second with a hope that it may also be useful for some extensions related to homogenization and averaging.

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Alexander Veretennikov
Affiliation: University of Leeds, UK — and — National Research University Higher School of Economics, and Institute for Information Transmission Problems, Moscow, Russia

Keywords: SDE, large deviations, Poisson equation, potential, exponential bounds
Received by editor(s): October 30, 2016
Published electronically: February 28, 2018
Additional Notes: This work was prepared within the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program, and supported by the RFBR grant 14-01-00319-a. Also, the author thanks the anonymous referee for useful remarks.
Article copyright: © Copyright 2018 American Mathematical Society

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