About this Title
Vladimir I. Bogachev, Moscow State University, Moscow, Russia, Nicolai V. Krylov, University of Minnesota, Minneapolis, MN, Michael Röckner, Bielefeld University, Bielefeld, Germany and Stanislav V. Shaposhnikov, Moscow State University, Moscow, Russia
Publication: Mathematical Surveys and Monographs
Publication Year 2015: Volume 207
ISBNs: 978-1-4704-2558-6 (print); 978-1-4704-2793-1 (online)
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.
Graduate students and researchers interested in partial differential equations and stochastic processes.
Table of Contents
- Chapter 1. Stationary Fokker–Planck–Kolmogorov equations
- Chapter 2. Existence of solutions
- Chapter 3. Global properties of densities
- Chapter 4. Uniqueness problems
- Chapter 5. Associated semigroups
- Chapter 6. Parabolic Fokker–Planck–Kolmogorov equations
- Chapter 7. Global parabolic regularity and upper bounds
- Chapter 8. Parabolic Harnack inequalities and lower bounds
- Chapter 9. Uniquess of solutions to Fokker–Planck–Kolmogorov equations
- Chapter 10. The infinite-dimensional case