"Stochastic Tools in Mathematics and Science"
covers basic stochastic tools used in physics,
chemistry, engineering and the life sciences. The topics
covered include conditional expectations, stochastic
processes, Brownian motion and its relation to partial
differential equations, Langevin equations, the
Liouville and Fokker-Planck equations, as well as Markov
chain Monte Carlo algorithms, renormalization, basic
statistical mechanics, and generalized Langevin
equations and the Mori-Zwanzig formalism. The
applications include sampling algorithms, data
assimilation, prediction from partial data, spectral
analysis, and turbulence. The book is based on lecture
notes from a class that has attracted graduate and
advanced undergraduate students from mathematics and
from many other science departments at the University of
California, Berkeley. Each chapter is followed by
exercises. The book will be useful for scientists and
engineers working in a wide range of fields and
applications. For this new edition the material has been
thoroughly reorganized and updated, and new sections on
scaling, sampling, filtering and data assimilation,
based on recent research, have been added. There are
additional figures and exercises. Review of earlier
edition: "This is an excellent concise textbook which
can be used for self-study by graduate and advanced
undergraduate students and as a recommended textbook for
an introductory course on probabilistic tools in
science." Mathematical Reviews, 2006
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