Markov Processes
An Introduction for Physical Scientists
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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.
Key Features
- A self-contained, prgamatic exposition of the needed elements of random variable theory
- Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations
- Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples
- Clear treatments of first passages, first exits, and stable state fluctuations and transitions
- Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics
Readership
Professionals/scientists without training in probability and statistics (using books as a "self-help" guide), senior undergraduate and graduate level students in physics and chemistry and mathematicians specializing in game theory, and finite math
Table of Contents
- Random Variable Theory. General Features of a Markov Process. Continuous Markov Processes. Jump Markov Processes with Continuum States. Jump Markov Processes with Discrete States. Temporally Homogeneous Birth-Death Markov Processes. Appendixes: Some Useful Integral Identities. Integral Representations of the Delta Functions. An Approximate Solution Procedure for "Open" Moment Evolution Equations. Estimating the Width and Area of a Function Peak. Can the Accuracy of the Continuous Process Simulation Formula Be Improved? Proof of the Birth-Death Stability Theorem. Solution of the Matrix Differential Equation. Bibliography. Index.
Product details
- No. of pages: 592
- Language: English
- Copyright: © Academic Press 1991
- Published: October 8, 1991
- Imprint: Academic Press
- Hardcover ISBN: 9780122839559
- eBook ISBN: 9780080918372
About the Author
Daniel Gillespie
Affiliations and Expertise
Naval Weapons Center