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This course introduces basic techniques for modelling and analysing systems in the presence of uncertainty. It will cover Poisson processes, discrete and continuous Markov chains, martingales, Brownian motions, stochastic calculus and its applications in financial engineering.
The book introduces the reader to elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research.
This lively introduction to measure-theoretic probability theory covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. Concentrating on results that are the most useful for applications, this comprehensive treatment is a rigorous graduate text and reference. Operating under the philosophy that the best way to learn probability is to see it in action, the book contains extended examples that apply the theory to concrete applications.
The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.
This book contains material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations, and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs.
This new edition showcases a focus on modeling and computation for complex classes of approximate dynamic programming problems
