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Advanced Stochastic Processes
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  • Title Advanced Stochastic Processes
  • Author(s) Jan A. Van Casteren
  • Publisher: BookBoon, University of Waterloo (2013)
  • Hardcover/Paperback N/A
  • eBook PDF (400+ pages)
  • Language: English
  • ISBN-10/ASIN: N/A
  • ISBN-13: 978-8740303988
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Book Description

This comprehensive guide to Stochastic Processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers.

In this book, which is basically self-contained, the following topics are treated thoroughly: Brownian motion as a Gaussian process, Brownian motion as a Markov process, and Brownian motion as a martingale. Brownian motion can also be considered as a functional limit of symmetric random walks, which is, to some extent, also discussed.

Related topics which are treated include Markov chains, renewal theory, the martingale problem, Ito calculus, cylindrical measures, and ergodic theory. Convergence of measures, stochastic differential equations, Feynman-Kac semigroups, and the Doob-Meyer decomposition theorem theorem are discussed in the second part of the book.

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