Brownian Motion And Its Applications to Mathematical Analysis

by Hiroyuki Matsumoto (Author), Setsuo Taniguchi (Author)

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.

"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences.