| Description |
1 online resource (312 pages) |
| Series |
London Mathematical Society lecture note series, 0076-0552 ; 54 |
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London Mathematical Society lecture note series ; 54. 0076-0552
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| 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 |
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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 |
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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 |
| 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 |
| Notes |
"Most of the papers compiled in this volume have been published in Uspekhi Matematicheskikh Nauk and translated into English in the Russian Mathematical Surveys"--Preface |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Markov processes.
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Stochastic analysis.
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MATHEMATICS -- Probability & Statistics -- Stochastic Processes.
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Markov processes
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Stochastic analysis
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Markov-Prozess
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Markov-processen.
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Stochastische analyse.
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| Form |
Electronic book
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| ISBN |
9781107361119 |
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1107361117 |
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9780511662416 |
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0511662416 |
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