Stochastic processes including birth, death, Yule, Polya and divergent processes

Abstract

Abstract Several articles in the Encyclopedia of Biostatistics describe various topics in stochastic process, while the present paper covers the main elements of the field, such as random walk, gambler's ruin, Markov chains, a general birth process, an equality in stochastic processes, death process and survival distribution, staging process, birth–death processes, and finite Markov processes. These topics together constitute an adequate representation of the field. The main feature of this article is the explicit solution for every process presented, especially the K‐M epidemic model, the higher order transition probabilities in Markov chains, and the explicit solution for the Kolmogorov differential equations. These solutions make it easy for the application of stochastic processes in research in biostatistics, epidemiology, health care, and medical sciences.