Markov Processes: An Introduction for Physical Scientists

ISBN-13: 9780122839559 / Angielski / Twarda / 1991 / 592 str.

Daniel T. Gillespie

Opis

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

Spis treści

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