Markov Processes

Name: Markov Processes | Volume II
Brand: Springer
Price: 53.49 EUR
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Volume II

E. B. Dynkin(Autor*in)

Springer (Verlag)

Erschienen am 18. August 2022

VIII, 276 Seiten

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Inhalt

Cover
Title page
Copyright page
Contents
Chapter Twelve
Excessive, superharmonic and harmonic functions
§ 1. Excessive functions for transition functions
§ 2. Excessive functions for Markov processes
§ 3. Asymptotic behavior of excessive functionsalong trajectories of a process
§ 4. Superharmonie functions
§ 5. Harmonie functions
Chapter Thirteen
Harmonie and superharmonic functions associated withstrong Feller processes. Probabilistic solution of certainequations
§ 1. Some properties of strong Feller processes
§ 2. The Dirichlet problems. Regular points of the boundary
§ 3. Harmonie and superharmonic functionsassociated with diffusion processes
§ 4. Solutions of the equation ztf- Vf= -g
§ 5. Parts of a diffusion process and Green's functions
Chapter Fourteen
The multi-dimensional Wiener processand its transformations
§ 1. Harmonie and superharmonic functionsrelated to the Wiener process
§ 2. The mapping 'l'
§ 3. Additive functionals and Green's functions
§ 4. Brownian motion with killing measure µ and speed measure v
§ 5. q-subprocesses
Chapter Fifteen
Continuous strong Markov processes on a closed interval
§ 1. General properties of one-dimensional continuous strong Markov processes
§ 2. Characteristics of regular processes
§ 3. Computation of the characteristic and infinitesimal operators
§ 4. Superharmonie and harmonic functionsconnected with regular one-dimensional processes
Chapter Sixteen
Continuous strong Markov processes on an open interval
§ 1. Harmonie functions and behavior of trajectories
§ 2. S-functions and character of the motion along a trajectory
§ 3. Infinitesimal operators
Chapter Seventeen
Construction of one-dimensional continuous strong Markov processes
§ 1. Transformations of the state space. Canonical coordinate
§ 2. Construction of regular continuous strong Markov processeson an open interval
§ 3. Construction of regular continuous strong Markov processeson a closed interval
§ 4. Computation of the harmonic functions and resolvents for regular processes
Appendix
§ 1. Measurable spaces and measurable transformations
§ 2. Measures and integrals
§ 3. Probability spaces. Conditional probabilities and mathematical expectations
§ 4. Martingales
§ 5. Topological measurable spaces
§ 6. Some theorems on partial differential equations
§ 7. Measures and countably additive set functions on the line and corresponding point functions
§ 8. Convex functions
Historical - Bibliographical note
Bibliography
Index
List of symbols

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