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Semigroups, Boundary Value Problems and Markov Processes (Hardcover, 2nd ed. 2014)
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Semigroups, Boundary Value Problems and Markov Processes (Hardcover, 2nd ed. 2014)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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 elliptic boundary value problems
for second-order, Waldenfels integro-differential operators in
partial differential equations and proves that this class of
elliptic boundary value problems provides a general class of Feller
semigroups in functional analysis. As an application, the author
constructs a general class of Markov processes in probability in
which a Markovian particle moves both by jumps and continuously in
the state space until it 'dies' at the time when it reaches the set
where the particle is definitely absorbed. Augmenting the 1st
edition published in 2004, this edition includes four new chapters
and eight re-worked and expanded chapters. It is amply illustrated
and all chapters are rounded off with Notes and Comments where
bibliographical references are primarily discussed. Thanks to the
kind feedback from many readers, some errors in the first edition
have been corrected. In order to keep the book up-to-date, new
references have been added to the bibliography. Researchers and
graduate students interested in PDEs, functional analysis and
probability will find this volume useful.
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