Semigroups, Boundary Value Problems and Markov Processes

• Κύριος συγγραφέας: Taira, Kazuaki (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
• Έκδοση: 2nd ed. 2014.
• Σειρά: Springer Monographs in Mathematics,
• Θέματα: Mathematics.; Harmonic analysis.; Functional analysis.; Partial differential equations.; Probabilities.; Functional Analysis.; Abstract Harmonic Analysis.; Partial Differential Equations.; Probability Theory and Stochastic Processes.

A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of ellipt...

Πίνακας περιεχομένων:

• 1.Introduction and Main Results
• Part I Elements of Analysis
• 2.Elements of Probability Theory
• 3.Elements of Functional Analysis
• 4.Theory of Semigroups
• Part II Elements of Partial Differential Equations
• 5.Theory of Distributions
• 6.Sobolev and Besov Spaces
• 7.Theory of Pseudo-Differential Operators
• 8.Waldenfels Operators and Maximum Principles
• Part III Markov Processes, Semigroups and Boundary Value problems
• 9.Markov Processes, Transition Functions and Feller Semigroups
• 10.Feller Semigroups and Elliptic Boundary Value Problems
• 11.Proof of Theorem 1.3
• 12.Markov Processes Revisited
• 13.Concluding Remarks
• Appendix: Boundedness of Pseudo-Differential Operators
• References
• Index.