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＜E-Book＞
Stochastic Tools in Mathematics and Science / by Alexandre J. Chorin, Ole H Hald
(Surveys and Tutorials in the Applied Mathematical Sciences. ISSN:21994773 ; 1)

Edition	2nd ed. 2009.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2009
Language	English
Size	X, 162 p. 7 illus : online resource
Authors	*Chorin, Alexandre J author Hald, Ole H author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:System theory LCSH:Physics LCSH:Mathematics LCSH:Fluid mechanics LCSH:Mathematical physics FREE:Probability Theory FREE:Complex Systems FREE:Classical and Continuum Physics FREE:Applications of Mathematics FREE:Engineering Fluid Dynamics FREE:Theoretical, Mathematical and Computational Physics
Notes	Preliminaries -- Probability -- Brownian Motion -- Stationary Stochastic Processes -- Statistical Mechanics -- Time-Dependent Statistical Mechanics Stochastic Tools in Mathematics and Science is an introductory book on probability-based modeling. It 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 and dimensional reduction, and basic equilibrium and non-equilibrium statistical mechanics. The applications include data assimilation, prediction from partial data, spectral analysis, and turbulence. A noteworthy feature of the book is the systematic analysis of memory effects. In this second edition, the new topics include Feynman diagrams and a new discussion of the renormalization group. 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. "Chorin and Hald provide excellent explanations with considerable insight and deep mathematical understanding, especially toward the end of the book in the context of simplified versions of the famous statistical mechanics models of Ising and of Mori and Zwanzig." (SIAM Review) HTTP:URL=https://doi.org/10.1007/978-1-4419-1002-8

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