Introduction to Stochastic Processes

An introduction to stochastic processes, which are random processes occurring in time or space. They are used to model dynamic relationships involving random events in a wide variety of disciplines including the natural and social sciences, and in financial, managerial and actuarial settings. The course consists of a short review of basic probability concepts and a discussion of conditional probability and conditional expectation, followed by an introduction to the basic concepts and an investigation of the long-run behaviour of Markov chains in discrete time, countable state space. The course also covers some important continuous-time stochastic processes including Poisson processes and other Markov pure jump processes, as well as Brownian motion and other related Gaussian processes as time permits.