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.
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.
From the reviews:
"The book is well-written and provides a very useful introduction to various areas of applications of stochastic processes."
(Evelyn Buckwar, Zentralblatt MATH, Vol. 1086, 2006)
"The authors write ... that this book is based on lecture notes for graduate courses on 'the stochastic methods of applied mathematics'. Their aim is ... to show various applications of probability to mathematics students and, on the other hand, to introduce nonmathematical students to the general ideas of probabilistic methods. ... 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."
(Mikhail V. Tretyakov, Mathematical Reviews, Issue 2006 j)
"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 Isign and of Mori and Zwanzig."
(SIAM Review) From the reviews of the second edition:
"In the second edition of the book by Alexandre J. Chorin and Ole H. Hald many parts of the text have been rewritten in order to clarify the presentation. ... The authors have added a short discussion on Feynman diagrams to the section on Wiener integrals. ... Also new exercises and figures have been added to the text. The new topics make the book even more useful as an introduction to stochastic modeling in the natural sciences and will certainly be appreciated by the readers."
(H. M. Mai, Zentralblatt MATH, Vol. 1184, 2010)
"The book is well-written and provides a very useful introduction to various areas of applications of stochastic processes."
(Evelyn Buckwar, Zentralblatt MATH, Vol. 1086, 2006)
"The authors write ... that this book is based on lecture notes for graduate courses on 'the stochastic methods of applied mathematics'. Their aim is ... to show various applications of probability to mathematics students and, on the other hand, to introduce nonmathematical students to the general ideas of probabilistic methods. ... 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."
(Mikhail V. Tretyakov, Mathematical Reviews, Issue 2006 j)
"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 Isign and of Mori and Zwanzig."
(SIAM Review) From the reviews of the second edition:
"In the second edition of the book by Alexandre J. Chorin and Ole H. Hald many parts of the text have been rewritten in order to clarify the presentation. ... The authors have added a short discussion on Feynman diagrams to the section on Wiener integrals. ... Also new exercises and figures have been added to the text. The new topics make the book even more useful as an introduction to stochastic modeling in the natural sciences and will certainly be appreciated by the readers."
(H. M. Mai, Zentralblatt MATH, Vol. 1184, 2010)