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.
Recenzijas
This is a well-written book. The authors are world experts in this area. The book contains many of their own results...This book is a highly valuable contribution to the literature on Fokker-Planck-Kolmogorov equations. It will certainly become a classic reference for researchers working in the field of partial differential equations and diffusion processes. Zhen-Qing Chen, Mathematical Reviews
Stationary Fokker-Planck-Kolmogorov equations
Existence of solutions
Global properties of densities
Uniqueness problems
Associated semigroups
Parabolic Fokker-Planck-Kolmogorov equations
Global parabolic regularity and upper bounds
Parabolic Harnack inequalities and lower bounds
Uniquess of solutions to Fokker-Planck-Kolmogorov equations
The infinite-dimensional case
Bibliography
Subject index
Vladimir I. Bogachev, Moscow State University, Russia.
Nicolai V. Krylov, University of Minnesota, Minneapolis, MN.
Michael Rockner, Bielefeld University, Germany.
Stanislav V. Shaposhnikov, Moscow State University, Russia.
