Stochastic Tools in Mathematics and Science [electronic resource] / by Alexandre Chorin, Ole H. Hald.

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).