Functional Analytic Techniques for Diffusion Processes

By Kazuaki Taira

Book Overview

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.

• Format: Hardcover
• Language: English
• ISBN: 9811910987
• ISBN13: 9789811910982
• Release Date: May 2022
• Publisher: Springer
• Length: 782 Pages
• Weight: 2.85 lbs.
• Dimensions: 1.7" x 6.1" x 9.2"