620-301 Stochastic Modelling

One of 620-201 or 620-203; and at least one of 620-112, 620-113, 620-122, 620-123, [98]620-130, [98]620-132, 620-142, 620-143, [99]620-200, 620-211.

This subject introduces the concept of a stochastic process and deals with the important standard stochastic processes, including Poisson process, Markov chains in discrete and continuous time (with some applications), renewal processes and time series. Students learn to understand, derive the behaviour and properties, and simulate simple stochastic process models derived from real-life situations. This subject demonstrates the importance of such models and in particular shows their applications to industry and the sciences.

Topics covered include review of the main concepts from probability theory, elements of utility theory, basic limit theorems, type of stochastic processes; analysis of Markov chains and their applications (elements of Markov decision processes); random walks; the Poisson and general jump Markov processes and their applications (with elements of queueing models); renewal theory; elements of time series (stationarity, filtering, basic linear models, identification and estimation); and elements of simulation, with basics of Markov chain Monte Carlo.

Up to 50 pages of written assignments; a 3-hour end-of-semester written examination; and class tests totalling not more than 1.5 hours.