Most existing books on evolution equations tend either to cover a
particular class of equations in too much depth for beginners or
focus on a very specific research direction. Thus, the field can be
daunting for newcomers to the field who need access to preliminary
material and behind-the-scenes detail. Taking an
applications-oriented, conversational approach, Discovering
Evolution Equations with Applications: Volume 2-Stochastic
Equations provides an introductory understanding of stochastic
evolution equations. The text begins with hands-on introductions to
the essentials of real and stochastic analysis. It then develops
the theory for homogenous one-dimensional stochastic ordinary
differential equations (ODEs) and extends the theory to systems of
homogenous linear stochastic ODEs. The next several chapters focus
on abstract homogenous linear, nonhomogenous linear, and
semi-linear stochastic evolution equations. The author also
addresses the case in which the forcing term is a functional before
explaining Sobolev-type stochastic evolution equations. The last
chapter discusses several topics of active research. Each chapter
starts with examples of various models. The author points out the
similarities of the models, develops the theory involved, and then
revisits the examples to reinforce the theoretical ideas in a
concrete setting. He incorporates a substantial collection of
questions and exercises throughout the text and provides two layers
of hints for selected exercises at the end of each chapter.
Suitable for readers unfamiliar with analysis even at the
undergraduate level, this book offers an engaging and accessible
account of core theoretical results of stochastic evolution
equations in a way that gradually builds readers' intuition.
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