Theory and Applications of Stochastic Processes: An Analytical Approach / Edition 1by Zeev Schuss
Pub. Date: 12/21/2009
Publisher: Springer New York
This book offers an analytical approach to shastic processes that are most common in the physical and life sciences. Its aim is to make probability theory readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and in asymptotic methods, rather than in probability and measure theory. It shows how to derive explicit expressions for quantities of interest by solving equations. Emphasis is put on rational modeling and approximation methods.
The book includes many detailed illustrations, applications, examples and exercises. It will appeal to graduate students and researchers in mathematics, physics and engineering.
Table of ContentsIntroduction.- The Physical Brownian Motion: Diffusion and Noise.- The Probability Space of Brownian Motion.- Ito Integration and Calculus.- Stochastic Differential Equations.- The Discrete Approach and Boundary Behavior.- The First Passage Time of Diffusions.- Markov Processes and Diffusion Approximations.- Diffusion Approximations to Langevin's Equation.- Large Deviations of Markovian Jump Processes.- Noise-Induced Escape from an Attractor.- Stochastic Stability.- Bibliography.
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