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Description
This module aims to provide an introduction to the study of systems which change state stochastically with time and to facilitate the development of skills in the application of probabilistic ideas. It is primarily intended for second and third year students registered on the undergraduate degree programmes offered by the Department of Statistical Science (including the MASS programmes).听For these students, the academic prerequisites for this module are met through compulsory study earlier in their programme. It also serves as an optional module for students taking the Mathematics and Statistics stream of the Natural Sciences degree (with prerequisite: STAT0005).
Intended Learning Outcomes
- understand the Markov property in discrete and continuous time;
- for discrete-time Markov chains, be able to find and classify the irreducible classes of intercommunicating states, calculate absorption or first passage times and probabilities, assess the equilibrium behaviour;
- for simple examples of continuous-time Markov chains, be able to write down the forward equations, find and interpret the equilibrium distribution.
Applications - Stochastic processes are vital to applications in finance and insurance, and have many applications in biology and medicine, and in the social sciences. They also play a fundamental role in areas such as queueing theory and the study of system reliability. The material in this module can be applied to simplified real-world situations, and provides the foundations for further study of more complex systems.
Indicative Content - Revision of conditional probability. Markov Chains (discrete time and states): transient and equilibrium behaviour, first passage times, classification of states, applications. Markov processes (continuous time, discrete states): general theory, forward and backward equations, equilibrium distributions; Poisson process, interval and counting properties; birth and death processes and other simple examples.
Key Texts - Available from .
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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