DOI 10.1007/s10958-018-3872-3 Journal of Mathematical Sciences, Vol. 232, No. 3, July, 2018 THE POISSON EQUATION AND ESTIMATES FOR DISTANCES BETWEEN STATIONARY DISTRIBUTIONS OF DIFFUSIONS V. I. Bogachev Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia email@example.com M. R¨ ockner Universit¨ at Bielefeld, Bielefeld 33501, Germany firstname.lastname@example.org S. V. Shaposhnikov Moscow State University, Moscow 119991, Russia National University Higher School of Economics 20, Myasnitskaya St., Moscow 101000, Russia St. Tikhon’s Orthodox Humanitarian University 23-5A, Novokuznetskaya St., Moscow 115184, Russia email@example.com UDC 517.95 We estimate distances between stationary solutions to Fokker–Planck–Kolmogorov equa- tions 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 so- lutions to satisfy the Poincar´e and logarithmic Sobolev inequalities. Bibliography:35 titles. Dedicated to the memory of Vasilii Vasil’evich Zhikov 1 Introduction Let us consider two Borel probability measures μ and σ on R satisfying the stationary Fokker– ∗ ∗ ∗ ∗ Planck–Kolmogorov equations L μ =0 and L σ =0, where L and L are formally adjoint μ σ μ σ
Journal of Mathematical Sciences – Springer Journals
Published: Jun 2, 2018
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