One of the simplest stochastic processes consists of sums of independent random variables. The first part of the course concerns limit theorems for such sums, especially the law of large numbers and the central limit theorem and their proofs.
The second part of the course deals with Markov chains. A Markov chain is a stochastic process in which predictions for the future depend only on the present state of affairs, but not on knowledge of past behaviour of the process. Markov chains have been used as models in many areas of science, management, and social science. We shall examine some of these applications, such as random walks, branching processes, and queueing models. We shall also study recurrence and transience of Markov chains.
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The final grade will be based on a combination of homework, tests, and a final exam.