Titlebook: Applied Probability; Kenneth Lange Textbook 20102nd edition The Editor(s) (if applicable) and The Author(s), under exclusive license to Sp

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Discrete-Time Markov Chains,astic component [23, 24, 59, 80, 106, 107, 118]. In this chapter we give a few examples and a quick theoretical overview of discrete-time Markov chains. The highlight of our theoretical development, Proposition 7.4.1, relies on a coupling argument. Because coupling is one of the most powerful and in

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Continuous-Time Markov Chains,e useful than discrete-time chains. For one thing, continuous-time chains permit variation in the waiting times for transitions between neighboring states. For another, they avoid the annoyances of periodic behavior. Balanced against these advantages is the disadvantage of a more complex theory invo

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Martingales,strategies to beat the house. Probabilists know better. The real payoff with martingales is their practical value throughout probability theory. This chapter introduces martingales, develops some relevant theory, and delves into a few applications. As a prelude, readers are urged to review the mater

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Diffusion Processes,n elementary level, stressing intuition rather than rigor. Readers with the time and mathematical inclination should follow up this brief account by delving into serious presentations of the mathematics [80, 107]. A good grounding in measure theory is indispensable in understanding the theory. At th

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Textbook 20102nd editiond examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential e