[PDF] Markov processes: An introduction to physical scientists Daniel T. Gillespie

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