Markov Processes: An Introduction for Physical Scientists

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 theoryLogically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equationsDetailed exposition of Monte Carlo simulation methods, with plots of many numerical examplesClear treatments of first passages, first exits, and stable state fluctuations and transitionsCarefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

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