Markov processes and related problems of analysis / E.B. Dynkin.

Format:

Book

Author/Creator:

Dynkin, E. B. (Evgeniĭ Borisovich), 1924-2014, author.

Series:

London Mathematical Society lecture note series ; 54.

London Mathematical Society lecture note series ; 54

Language:

English

Subjects (All):

Markov processes.

Stochastic analysis.

Physical Description:

1 online resource (312 pages) : digital, PDF file(s).

Other Title:

Markov Processes & Related Problems of Analysis

Place of Publication:

Cambridge : Cambridge University Press, 1982.

Language Note:

English

Summary:

The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Contents:

Cover; Title; Copyright; Contents; Preface; References; MARKOV PROCESSES AND RELATED PROBLEMS OF ANALYSIS; 1. Introduction; 2. General problems in the theory of Markov processes; 3. The form of an Infinitesimal operator. Generalized diffusion processes; 4. Harmonic, subharmonic, and superharmonic functions associated with a Markov process; 5. Additive functionals and associated transformations of Markov process; 6. Stochastic integral equations; 7. Boundary problems in the theory of differential equations and the asymptotic behaviour of trajectories; 8. Concluding remarks; References

MARTIN BOUNDARIES AND NON-NEGATIVE SOLUTIONS OF A BOUNDARY VALUE PROBLEM WITH A DIRECTIONAL DERIVATIVEIntroduction; 1. Boundary value problems for Laplace's equation and the Martin boundary; 2. Cones in linear topological spaces; 3. The boundary value problem with a directional derivative (Problem A); 4. Reduction of Problem fi - some particular solutions; 5. The Minimum Principle and its consequences; 6. The Green's Function; 7. Asymptotic behaviour of the Green's function

8. The Martin boundary for the boundary value problem A. A description of the non-negative solutions and the solutions bounded belowReferences; BOUNDARY THEORY OF MARKOV PROCESSES (THE DISCRETE CASE); 1. Harmonic and excessive functions and measures; 2. Markov processes; 3. The Green's function; 4. Supermartingales; 5. Excessive functions and supermartingales; 6. Position of a particle at the last exit time from a set D; 7. Densities of excessive measures and supermartingales; 8. Excessive measures with densities of class Kγ.The Martin kernel; 9. Martin compactification

10. Distribution of11. /z-processes. Martin representation of excessive functions; 12. The spectral measure of kz. The exit space; 13. The Uniqueness Theorem; 14. Minimal excessive functions; 15. The operator θ. Final random variables; 16. The entrance space. Decomposition of excessive measures; 17. The behaviour of a stationary process as; 18. Stationary processes with random birth and death times; 19. Hunt processes; Appendix Measures in spaces of paths; References; THE INITIAL AND FINAL BEHAVIOUR OF TRAJECTORIES OF MARKOV PROCESSES; 1. Introduction

2. Decomposition into ergodic measures3. Construction of a Kernel; 4. The entrance space and the exit space; 5. Markov processes with random birth and death times; References; INTEGRAL REPRESENTATION OF EXCESSIVE MEASURES AND EXCESSIVE FUNCTIONS; 1. Plan of the paper. Discussion of results; 2. The construction of a Markov process from an excessive measure and function; 3 Excessive measures; 4. Excessive functions; 5 Homogeneous excessive functions; 6 The faces of the simplex Kp. Invariant and nullexcessive measures and functions. The entrance laws

7 Excessive functions and supermartingales

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88401-8

1-107-36602-X

1-107-37075-2

1-107-36111-7

1-107-36976-2

1-299-40382-4

1-107-36356-X

0-511-66241-6