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Synopsis
This book is designed for a graduate course in stochastic processes. It is written for the reader who is familiar with measure-theoretic probability and the theory of discrete-time processes who is now ready to explore continuous-time stochastic processes. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a Markov process and a martingale in continuous time. The authors show how, by means of stochastic integration and random time change, all continuous martingales and many continuous Markov processes can be represented in terms of Brownian motion. The text is complemented by a large number of exercises.
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Second Edition
I. Karatzas and S.E. Shreve
Brownian Motion and Stochastic Calculus
"A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."―MATHEMATICAL REVIEWS
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Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics 113
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