Nonlinear Markov Processes and Kinetic Equations

Erscheinungsjahr 2010
ISBN: 978-0-521-11184-3
Verlag: Cambridge University Press

Buch, Englisch, Band 182, 394 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 720 g

Reihe: Cambridge Tracts in Mathematics

• Presents a multidimensional view of the subject by exploring different methods
• End-of-chapter exercises enable the reader to test their understanding
• Applications of these processes include non-equilibrium statistical mechanics, evolutionary biology, population and disease dynamics, and dynamics of economic and social systems
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Ist careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.

Autoren/Hrsg.

Kolokoltsov, Vassili N.

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biophysik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Naturwissenschaften Physik Angewandte Physik Biophysik

Inhaltsverzeichnis

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 Lévy–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.

Über Autor(innen)

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