A Course in Applied Stochastic Processes

This book is an introduction to applications of the theory of stochastic processes--more specifically Markov chain theory--in population dynamics, genetics, and epidemics. A prior exposure to basic probability theory should be helpful, but by no means essential. The book includes a quick review of probability that starts from elementary combinatorial probability and ends with some basic properties of diffusions, including a fairly extensive account of martingales and Markov chains, mostly with proofs. This is done fairly rigorously without using measure theoretic tools. In continuation of the effort to keep the prerequisites at the bare minimum, all the basic genetics the reader needs to know is included. Yet sophisticated material on Wright-Fisher and Moran models of genetics, including diffusion approximations, is presented. The material on epidemic models includes several important threshold theorems with carefully presented interpretation and complete proofs. Although this book is primarily intended for use as a textbook for a course on applied stochastic processes, it can also be used by researchers in the fields of genetics or epidemics for learning about applications of probability in their respective areas.