http://www.springer.com/math/probability/book/978-1-4419-1001-1

http://www.amazon.com/Stochastic-Mathematics-Tutorials-Mathematical-Sciences/dp/1441910018


Stochastic Tools in Mathematics and Science (Surveys and Tutorials in the Applied Mathematical Sciences)
By Alexandre J. Chorin, Ole H. Hald

Publisher:   Springer
Number Of Pages:   162
Publication Date:   2009-08-07
ISBN-10 / ASIN:   1441910018
ISBN-13 / EAN:   9781441910011

Product Description:

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. The presentation is mathematically attractive, and should form a useful bridge between the theoretical treatments familiar to mathematical specialists and the more practical questions raised by specific applications.
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.

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Summary: A great "user's guide" to stochastic calculus and its important applications
Rating: 5
This is an excellent user's guide to stochastic calculus and its important applications. I say excellent because it is well-written (clear and easy to read with a focus on the essentials as previous review said). I say "user's guide" because the author's get down to the nut's and bolt's of stochastic processes (concepts and related equations). I say "important applications" because they again focus on key "tools" such as Fokker-Planck equation and related stochastic differential equation, statistical mechanics, MCMC, turbulence, etc. - so there is something for everyone here e.g. physicists, financial "engineers", ME's and Aero's simulating turbulence (especially via PDF methods), etc. A few criticisms would be lack of "pixels" - they say a picture tell's a thousand words for a reason, hard to locate a term or definition or concept from index,...Overall, a very nicely priced/sized read and a must have reference for anyone working with stochastic processes seeking insight.

Summary: The Essentials
Rating: 5
This book was written to fill in the gaps between what people learn in standard "pure" math trainings and what people use "in the field". The professors who wrote it come from a University where one can study math and never see topics from statistical sciences. They have attempted a very readable and clear exposition of some of the fundamentals behind the useful stochastic analysis in physics and economics. They use some formalism but largely skip long, difficult proofs, focusing instead on important examples. What I mean is they use the language of formal probability theory (measure theory), but keep the applications very concrete (differential equations, stochastic walks, etc). It cuts to the chase and is an exciting read for those like myself who get very turned off by overly formal probability theory, yet who are curious about some of the formalism. Short, paperback, good references, lively read.