On Poisson equations with a potential in the whole space for “ergodic” generators
Author:
Alexander Veretennikov
Journal:
Theor. Probability and Math. Statist. 95 (2017), 195-206
MSC (2010):
Primary 60--02; Secondary 60J60, 60J45, 35J15
DOI:
https://doi.org/10.1090/tpms/1029
Published electronically:
February 28, 2018
MathSciNet review:
3631651
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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.
References
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References
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- N. V. Krylov, On Itô stochastic integral equations, Theory Probab. Appl. 14 (1969), no. 2, 330–336. MR 0270462
- N. V. Krylov, Controlled Diffusion Processes, 2nd ed., Springer Science & Business Media, 2008. MR 2723141
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Additional Information
Alexander Veretennikov
Affiliation:
University of Leeds, UK — and — National Research University Higher School of Economics, and Institute for Information Transmission Problems, Moscow, Russia
Email:
a.veretennikov@leeds.ac.uk
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.
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© Copyright 2018
American Mathematical Society
