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 conditionalexpectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planckequations, as well as Markov chain Monte Carlo algorithms, renormalization and dimensional reduction, and basic equilibrium and non-equilibrium statisticalmechanics. The applications include data assimilation, prediction from partial data, spectral analysis, and turbulence. A noteworthy feature of the book isthe systematic analysis of memory effects. The presentation is mathematicallyattractive, and should form a useful bridge between the theoretical treatments familiar to mathematical specialists and the more practical questions raisedby 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. INDICE: Preliminaries.- Probability.- Brownian Motion.- Stationary Stochastic Processes.- Statistical Mechanics.- Time-Dependent Statistical Mechanics.
- ISBN: 978-1-4419-1001-1
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 162
- Fecha Publicación: 01/08/2009
- Nº Volúmenes: 1
- Idioma: Inglés