Elliptic Boundary Value Problems and Construction of Lp-Strong Feller Processes with Singular Drift and Reflection

ISBN-13: 9783658058289 / Angielski / Miękka / 2014 / 198 str.

Benedict Baur

Opis

Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of Lp-strong Feller processes using Dirichlet form methods, regularity for solutions of elliptic boundary value problems, construction of elliptic diffusions with singular drift and reflection, Skorokhod decomposition and applications to Mathematical Physics like finite particle systems with singular interaction. Emphasize is placed on the handling of singular drift coefficients, as well as on the discussion of point wise and path wise properties of the constructed processes rather than just the quasi-everywhere properties commonly known from the general Dirichlet form theory.

Recenzje

"The author presents modern functional analytic methods for the construction and analysis of Feller processes in general and diffusion processes in particular. ... This book is a must-read for people who are interested in (stochastic) differential equations, Dirichlet forms, stochastic processes and their applications." (J. A. Van Casteren, Mathematical Reviews, November, 2015)

Spis treści

​Introduction.- Construction of Lp-Strong Feller Processes.- Elliptic Regularity up to the Boundary.- Construction of Elliptic Diffusions.- Applications.- Construction of the Local Time and Skorokhod Decomposition.- Appendix.

O autorze

Benedict Baur has done his doctor’s degree at the University of Kaiserslautern in topics on Stochastics and Functional Analysis.

Blurb

Benedict Baur presents modern functional analytic methods for construction and analysis of Feller processes in general and diffusion processes in particular. Topics covered are: Construction of L^p-strong Feller processes using Dirichlet form methods, regularity for solutions of elliptic boundary value problems, construction of elliptic diffusions with singular drift and reflection, Skorokhod decomposition and applications to Mathematical Physics like finite particle systems with singular interaction. Emphasize is placed on the handling of singular drift coefficients, as well as on the discussion of pointwise and pathwise properties of the constructed processes rather than just the quasi-everywhere properties commonly known from the general Dirichlet form theory.

Contents

• Construction of L^p-Strong Feller Processes
• Elliptic Boundary Value Problems
• Skorokhod Decomposition for Reflected Diffusions with Singular Drift
• Particle Systems with singular interaction

Target Groups

Graduate and PhD students, researchers of Mathematics in the field (Functional) Analysis, Stochastics, Partial Differential Equations and Mathematical Physics

The Author

Benedict Baur has done his doctor’s degree at the University of Kaiserslautern in topics on Stochastics and Functional Analysis.