The theory of stochastic processes is concerned with systems which change in accordance with probability laws. It can be regarded as the "dynamic" part of statistic theory. Many applications occur in physics, engineering, computer sciences, economics, financial mathematics and biological sciences, as well as in other branches of mathematical analysis such as partial differential equations. The purpose of this course is to provide an introduction to the many specialized treatise on stochastic processes. Most of this course is on discrete state spaces. It is a second course in probability which should be of interest to students of mathematics and statistics as well as students from other disciplines in which stochastic processes have found significant applications. Special efforts will be made to attract and interest students in the rich diversity of applications of stochastic processes and to make them aware of the relevance and importance of the mathematical subtleties underlying stochastic processes.
The material is divided between discrete and continuous processes. However, most emphasis is on discrete stochastic processes for which the general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics including Random Walk, Markov Processes, Continuous Time Markov Chains, Poisson Processes and Birth-death Processes, Renewal Theory and Queues, Martingales and Optional Sampling, Brownian Motion, Ito’s Lemma will be covered. These topics will be chosen among the different sections of the text book.
Required: Sheldon Ross, Introduction to Probability Models, 10th Edition, Academic Press, ISBN:0125980620.
Optional: G. Grimmett and D. Stirzaker, Probability and Random Processes, 3rd edition, Oxford University Press, ISBN: 0198572220.
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MATH 525 or equivalent. Good understanding of basic probability theory including: Random variables, expectation, independence, conditional probability and expectation, and advanced calculus covering limits, series, the notion of continuity, differentiation and the Riemann integral, and Linear algebra including eigenvalues and eigenfunctions is crucial.
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