Chiang C.L. Introduction to Stochastic Processes in Biostatistics

New York: John Wiley&sons, 1968. — 342 p.Time, life, and risks are three basic elements of stochastic processes in biostatistics. Risks of death, risks of illness, risks of birth, and other risks act continuously on man with varying degrees of intensity. Long before the development of modern probability and statistics, men were concerned with the chance of dying and the length of life, and they constructed tables to measure longevity. But it was not until the advances in the theory of stochastic processes made in recent years that empirical processes in the human population have been systematically studied from a probabilistic point of view. The purpose of this book is to present stochastic models describing these empirical processes. Emphasis is placed on specific results and explicit solutions rather than on the general theory of stochastic processes. Those readers who have a greater curiosity about the theoretical arguments are advised to consult the rich literature on the subject.
A basic knowledge of probability and statistics is required for a profit- able reading of the text. Calculus is the only mathematics presupposed, although some familiarity with differential equations and matrix algebra is needed for a thorough understanding of the material.
The text is divided into two parts. Part 1 begins with one chapter on random variables and one on probability generating functions for use in succeeding chapters. Chapter 3 is devoted to basic models of population growth, ranging from the Poisson process to the time-dependent birth- death process. Some other models of practical interest that are not in- cluded elsewhere are given in the problems at the end of the chapter.