Real Analysis Methods for Markov Processes Singular Integrals and Feller Semigroups /
This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called the Waldenfels operator, in the int...
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| Coauteur: | |
| Formaat: | Elektronisch E-boek |
| Taal: | Engels |
| Gepubliceerd in: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2024.
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| Editie: | 1st ed. 2024. |
| Onderwerpen: | |
| Online toegang: | https://doi.org/10.1007/978-981-97-3659-1 |
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Inhoudsopgave:
- Introduction and Main Results
- Elements of Functional Analysis
- Elements of Measure Theory and Lp Spaces
- Elements of Real Analysis
- Harmonic Functions and Poisson Integrals
- Besov Spaces via Poisson Integrals
- Sobolev and Besov Spaces
- Maximum Principles in Sobolev Spaces
- Elements of Singular Integrals
- Calder´on–Zygmund Kernels and Their Commutators
- Calder´on–Zygmund Variable Kernels and Their Commutators
- Dirichlet Problems in Sobolev Spaces
- Calder´on–Zygmund Kernels and Interior Estimates
- Calder´on–Zygmund Kernels and Boundary Estimates
- Unique Solvability of the Homogeneous Dirichlet Problem
- Regular Oblique Derivative Problems in Sobolev Spaces
- Oblique Derivative Boundary Conditions
- Boundary Representation Formula for Solutions
- Boundary Regularity of Solutions
- Proof of Theorems 16.1 and 16.2
- Markov Processes and Feller Semigroups
- Feller Semigroups with Dirichlet Condition
- Feller Semigroups with an Oblique Derivative Condition
- Feller Semigroups and Boundary Value Problems
- Feller Semigroups with a First Order Ventcel’ Boundary Condition
- Concluding Remarks.