ENGLISH

Brownian Motion and Potential Theory, Modern and Classical

By Murali Rao , Palle Jorgensen , James Tian

Book information

Publisher
World Scientific
Year
2024
ISBN
9789811294310, 9789811294778, 9789811294327, 9789811294334
DOI
10.1142/13872
Language
english
Format
PDF
Filesize
5 MB (5600610 bytes)
Series
Contemporary Mathematics and Its Applications 9
Edition
1
Pages
260\261
Topic
Mathematics\\Analysis
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-11-08 11:34:28
Brownian MotionCapacatiesDirichlet SpacesGreen FunctionsHarmonic FunctionsOperator Semi-GroupsPotential OperatorsRiesz Measures

Description

In this book, potential theory is presented in an inclusive and accessible manner, with the emphasis reaching from classical to modern, from analytic to probabilistic, and from Newtonian to abstract or axiomatic potential theory (including Dirichlet spaces). The reader is guided through stochastic analysis featuring Brownian motion in its early chapters to potential theory in its latter sections. This path covers the following themes: martingales, diffusion processes, semigroups and potential operators, analysis of super harmonic functions, Dirichlet problems, balayage, boundaries, and Green functions. The wide range of applications encompasses random walk models, especially reversible Markov processes, and statistical inference in machine learning models. However, the present volume considers the analysis from the point of view of function space theory, using Dirchlet energy as an inner product.

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