This course is an introduction to the field of stochastic processes, which are ordered collections of (generally dependent) random variables, usually indexed by either time or space. They are used to model dynamic relationships involving random events in a wide variety of disciplines including engineering, the natural and social sciences as well as financial, managerial and actuarial settings.

The course consists of four parts. The first consisting of a short review of basic probability concepts and a discussion of conditional probability and conditional expectation. The second and third, which will comprise the majority of the lectures, present an introduction to the basic concepts and an investigation of the long-run behaviour, respectively, of simple stochastic processes in discrete time; namely, Markov chains. Finally, the fourth section will be comprised of various topics regarding some important forms of 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.

To achieve an understanding of and facility in:

• Basic concepts and an investigation of the long-run behaviour, respectively, of simple stochastic processes in discrete time; namely, Markov chains.
• Various topics regarding some important forms of continuous-time stochastic processes including
  • Poisson processes
  • other Markov pure jump processes
  • Brownian motion
  • other related Gaussian processes.

• Mid-semester assignment 20%
• Final exam (3 hours) 80%

Three contact hours per week plus private study time.

STAT2001 Introductory Mathematical Statistics.

Please refer to Course Website