This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Fokker-planck-kolmogorov Equations (Mathematical Surveys and Monographs)

Science & Math

Vladimir I. Bogachev

Nicolai V. Krylov

Michael Röckner

Stanislav V. Shaposhnikov

Mathematics

American Mathematical Society

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Fokker–Planck–Kolmogorov Equations (Mathematical Surveys and Monographs, 207)

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Books by Nicolai V. Krylov