Abstract

This book is a final year undergraduate text on stochastic analysis, a theory used widely by statisticians and experts working, for example, in mathematical finance. A detailed treatment is given of conditional probability and expectation, a topic which is essential as a tool for stochastic processes. Exercises, complete with informal hints and fully worked solutions, are chosen as the main means of explanation, hence the course has a strong self-study element. The authors have concentrated on major topics within stochastic analysis: martingales in discrete time and their convergence, Markov chains, stochastic processes in continuous time, with emphasis on the Poisson process and Brownian motion, as well as Ito stochastic calculus including stochastic differential equations.

Contents

Chapter 1: Review of Probability Chapter 2: Conditional Expectation Chapter 3: Martingales in Discrete Time Chapter 4: Martingale Inequalities and Convergence Chapter 5: Markov Chains Chapter 6: Stochastic Processes in Continuous Time Chapter 7: Ito Stochastic Calculus

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Contact the authors

Would you like to make a comment or report a mistake? Your feedback will be greatly appreciated! Please e-mail the authors at: zb500@york.ac.uk or tz506@york.ac.uk Our postal address is: Department of Mathematics, University of York Heslington YO10 5DD, United Kingdom