This book offers an analytical approach to stochastic 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.
Author(s): Zeev Schuss (auth.)
Series: Applied Mathematical Sciences 170
Edition: 1
Publisher: Springer-Verlag New York
Year: 2010
Language: English
Pages: 468
Tags: Probability Theory and Stochastic Processes;Statistical Physics, Dynamical Systems and Complexity;Appl.Mathematics/Computational Methods of Engineering
Front Matter....Pages i-xvii
The Physical Brownian Motion: Diffusion And Noise....Pages 1-24
The Probability Space of Brownian Motion....Pages 25-62
ItĂ´ Integration and Calculus....Pages 63-91
Stochastic Differential Equations....Pages 92-132
The Discrete Approach and Boundary Behavior....Pages 133-175
The First Passage Time of Diffusions....Pages 176-206
Markov Processes and their Diffusion Approximations....Pages 207-256
Diffusion Approximations to Langevin’s Equation....Pages 257-301
Large Deviations of Markovian Jump Processes....Pages 302-338
Noise-Induced Escape From an Attractor....Pages 339-398
Stochastic Stability....Pages 399-441
Back Matter....Pages 442-468
