This is a second course in Probability Theory and Stochastic Processes. It assumes a background in elementary probability theory which will be reviewed and overviewed initially. The course then develops the necessary mathematics and intuition to understand discrete and continuous stochastic processes. Students will learn not merely results but proofs as well. This will help students firmly understand the underlying mathematics and provide the intuition for setting up a model in a specific application or a problem. These problems can be from diverse fields such as engineering, physics, operations research, economics, finance, or statistics.
Students learn and strengthen their understanding of basics of random variable, and the simplest and most important classes of stochastic processes, namely, Poisson, Gaussian and finite Markov chains.
Students learn about renewal theory which is a generalization of Poisson processes and will thoroughly learn the mathematical foundations of various results.
Students learn about generalization of Markov chains to countable state spaces and continuous time.
Students learn the basics of random walks and martingales, and their applications
Students will learn about real-world applicability of the theory set up.