AS/SC/AK/ MATH 4430 3.0 W

Stochastic Processes

      Basic stochastic processes, including Markov chains, Poisson processes, and birth- death processes. Topics from queues, renewal processes, stationary processes, Brownian motion.
      The course will trace the evolution of various areas of mathematics, such as analysis, algebra, and geometry. While it will involve a great deal of technical mathematics, the course will also explore issues closely bound up with its progress, such as the changing standards of rigor in mathematics, the cultural context of mathematics, the roles of problems and crises in the development of mathematics, and the roles of intuition and logic in its development.
      This course is an introduction to stochastic, or random, processes. Stochastic processes are models which represent phenomena that change in a random way over time. Simple examples are (a) the amount of money a gambler has after each play of a game and (b) the number of people waiting for service at a bank at various times. This course studies some of the most basic stochastic processes, including Markov chains and Poisson processes. 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 the past behaviour of the process. Markov chains are relatively easy to analyze, and they have been used as models in many areas of science, management, and social science. A Poisson process is a model for the occurrence of random events (such as oil spills in the Atlantic Ocean). This course will treat both the theory and applications of these stochastic processes.