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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Dedicated to the memory of Vasilii Vasil’evich Zhikov
Translated from Problemy Matematicheskogo Analiza 92, 2018, pp. 45-68.
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Bogachev, V.I., Röckner, M. & Shaposhnikov, S.V. The Poisson Equation and Estimates for Distances Between Stationary Distributions of Diffusions. J Math Sci 232, 254–282 (2018). https://doi.org/10.1007/s10958-018-3872-3
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DOI: https://doi.org/10.1007/s10958-018-3872-3