The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions


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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.

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V. Bogachev

Moscow State University; National University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University

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Email: vibogach@mail.ru
俄罗斯联邦, Moscow, 119991; 20, Myasnitskaya St., Moscow, 101000; 23-5A, Novokuznetskaya St., Moscow, 115184

M. Röckner

Universität Bielefeld

Email: vibogach@mail.ru
德国, Bielefeld, 33501

S. Shaposhnikov

Moscow State University; National University Higher School of Economics; St. Tikhon’s Orthodox Humanitarian University

Email: vibogach@mail.ru
俄罗斯联邦, Moscow, 119991; 20, Myasnitskaya St., Moscow, 101000; 23-5A, Novokuznetskaya St., Moscow, 115184

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