Markov Processes - 1st Edition - ISBN: 9780122839559, 9780080918372

Markov Processes

1st Edition

An Introduction for Physical Scientists

Authors: Daniel Gillespie
Hardcover ISBN: 9780122839559
eBook ISBN: 9780080918372
Imprint: Academic Press
Published Date: 8th October 1991
Page Count: 592
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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

@introbul:Key Features @bul:* 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


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.


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© Academic Press 1991
Academic Press
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About the Author

Daniel Gillespie

Affiliations and Expertise

Naval Weapons Center