数学と科学における確率論的手法 Stochastic Tools in Mathematics and Science (Surveys and Tutorials in the Applied Mathematical Sciences)

Chorin, Alexandre Joel/ Hald, Ole H.

Springer Verlag（2006/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 147 p.
• 言語 ENG
• 商品コード 9780387280806
• DDC分類 511

基本説明

An introductory book on probability-based modeling in mathematics and physics, in particular Brownian motion, Langevin equations, Liouville equations, statistical projections, renormalization, maximum likelihood estimation, expectation maximization, with applications to statistical mechanics, fluid mechanics, and neural computation.

Full 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.

Contents

Preliminaries.- Introduction to Probability.- Brownian Motion and Its Applications.- Stationary Stochastic.-Processes.- Statistical Mechanics.- Time-Dependent Statistical Mechanics.