Functional Analytic Techniques for Diffusion Processes /
This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (micro...
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| Format: | Book |
| Language: | English |
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Singapore :
Springer Nature Singapore : Imprint: Springer,
2022
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| Edition: | 1st ed. 2022 |
| Series: | Springer Monographs in Mathematics,
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Table of Contents:
- 1. Introduction and Summary
- Part I Foundations of Modern Analysis
- 2. Sets, Topology and Measures
- 3. A Short Course in Probability Theory
- 4. Manifolds, Tensors and Densities
- 5. A Short Course in Functional Analysis
- 6. A Short Course in Semigroup Theory
- Part II Elements of Partial Differential Equations. 7. Distributions, Operators and Kernels
- 8. L2 Theory of Sobolev Spaces
- 9. L2 Theory of Pseudo-Differential Operators
- Part III Maximum Principles and Elliptic Boundary Value Problems
- 10. Maximum Principles for Degenerate Elliptic Operators
- Part IV L2 Theory of Elliptic Boundary Value Problems
- 11. Elliptic Boundary Value Problems
- Part V Markov Processes, Feller Semigroups and Boundary Value Problems
- 12. Markov Processes, Transition Functions and Feller Semigroups
- 13. L2 Approach to the Construction of Feller Semigroups
- 14. Concluding Remarks
- Part VI Appendix
- A A Brief Introduction to the Potential Theoretic Approach
- References
- Index