Email this article The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions
- Authors: Bogachev V.I.1,2,3, Röckner M.4, Shaposhnikov S.V.1,2,3
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Affiliations:
- Moscow State University
- National University Higher School of Economics
- St. Tikhon’s Orthodox Humanitarian University
- Universität Bielefeld
- Issue: Vol 232, No 3 (2018)
- Pages: 254-282
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/241296
- DOI: https://doi.org/10.1007/s10958-018-3872-3
- ID: 241296
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Abstract
We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equations with different diffusion and drift coefficients. To this end we study the Poisson equation on the whole space. We have obtained sufficient conditions for stationary solutions to satisfy the Poincaré and logarithmic Sobolev inequalities.
About the authors
V. I. Bogachev
Moscow State University; National University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University
Author for correspondence.
Email: vibogach@mail.ru
Russian Federation, Moscow, 119991; 20, Myasnitskaya St., Moscow, 101000; 23-5A, Novokuznetskaya St., Moscow, 115184
M. Röckner
Universität Bielefeld
Email: vibogach@mail.ru
Germany, Bielefeld, 33501
S. V. Shaposhnikov
Moscow State University; National University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University
Email: vibogach@mail.ru
Russian Federation, Moscow, 119991; 20, Myasnitskaya St., Moscow, 101000; 23-5A, Novokuznetskaya St., Moscow, 115184
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