Essentials of Stochastic Processes

Designed for a Master's Level course in stochastic processes. This work features the introduction and use of martingales, which allow one to do much more with Brownian motion, such as, option pricing, and queueing theory is integrated into the Continuous Time Markov Chain and Renewal Theory chapters as examples.

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Stochastic processes have become important for many fields, including mathematical finance and engineering. Written by one of the worlds leading probabilists, this book presents recent results previously available only in specialized monographs. It features the introduction and use of martingales, which allow readers to do much more with Brownian motion, e.g., applications to option pricing, and integrates queueing theory into the presentation of continuous time Markov chains and renewal theory.