Basic Stochastic Processes

A Course Through Exercises


Z. Brzezniak and T. Zastawniak

Springer Undergraduate Series in Mathematics
Springer-Verlag, London 1999


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Springer catalogue entry

     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.

     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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