Brownian Motion And Potential Theory, Modern And Classical

Palle Jorgensen (The Univ Of Iowa, Usa), Murali Rao (Univ Of Florida, Usa), James Tian (American Mathematics Society, Usa)

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English

World Scientific Publishing Co Pte Ltd
15 November 2024

Complex analysis, complex variables; Functional analysis & transforms

Series: Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes

Summary
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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. This present volume is an expanded and revised version of an original set of lectures in the Aarhus University Mathematics Institute Lecture Note Series.

By: Palle Jorgensen (The Univ Of Iowa Usa), Murali Rao (Univ Of Florida, Usa), James Tian (American Mathematics Society, Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Volume: 9
ISBN: 9789811294778
ISBN 10: 9811294771
Series: Contemporary Mathematics And Its Applications: Monographs, Expositions And Lecture Notes
Pages: 260
Publication Date: 15 November 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active