Applied stochastic analysis
著者
書誌事項
Applied stochastic analysis
（Graduate studies in mathematics, v. 199）
American Mathematical Society, c2019
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注記
Includes bibliographical references (p. 289-299) and index
内容説明・目次
内容説明
This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.
目次
Fundamentals: Random variables
Limit theorems
Markov chains
Monte Carlo methods
Stochastic processes
Wiener process
Stochastic differential equations
Fokker-Planck equation
Advanced topics: Path integral
Random fields
Introduction to statistical mechanics
Rare events
Introduction to chemical reaction kinetics
Appendix
Bibliography
Index.
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