Markov Processes: An Introduction for Physical Scientists

by Daniel T. Gillespie

Overview

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.

• 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

Product Details

ISBN-13:	9780080918372
Publisher:	Elsevier Science
Publication date:	12/02/1991
Sold by:	Barnes & Noble
Format:	eBook
Pages:	592
File size:	10 MB

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

Editorial Reviews

Treats only univariate processes, and assumes no prior knowledge of probability and random variables, two concessions to the introductory purpose of the text. Assumes a working knowledge of differential and integral calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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