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Nonlinear Markov Processes and Kinetic Equations
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Table of Contents

Preface; Basic notations; 1. Introduction; Part I. Tools From Markov Processes: 2. Probability and analysis; 3. Probabilistic constructions; 4. Analytic constructions; 5. Unbounded coefficients; Part II. Nonlinear Markov Processes and Semigroups: 6. Integral generators; 7. Generators of Levy-Khintchine type; 8. Smoothness with respect to initial data; Part III. Applications to Interacting Particles: 9. The dynamic law of large numbers; 10. The dynamic central limit theorem; 11. Developments and comments; 12. Appendices; References; Index.

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A careful exposition of the most fundamental questions in the theory of nonlinear Markov processes.

About the Author

Vassili N. Kolokoltsov is a Reader in Probability in the Department of Statistics at the University of Warwick.

Reviews

'This monograph is suitable for graduate students and researchers who have a good background in probability theory and analysis and have mastered such key topics as martingales, stochastic calculus and weak convergence, on the one hand, and the analytic theory of semigroups, on the other hand. ... This book is pioneering in developing a new and important type of dynamics for modelling complex stochastic systems. It deserves to be widely read.' Bulletin of the London Mathematical Society
'... this is an important book. Written with great care by a leading expert, it is accessible to researchers and graduate students in stochastic and functional analysis, with applications in mathematical physics and systems biology.' Mathematical Reviews
"In the reviewer's opinion, this is an important book. Written with great care by a leading expert, it is accessible to researchers and graduate students in stochastic and functional analysis, with applications in mathematical physics and systems biology." M. Iosifescu, Mathematical Reviews
"This book is pioneering in developing a new and important type of dynamics for modelling complex stochastic systems. It deserves to be widely read." David Applebaum, Bulletin of the London Mathematical Society

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