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The subject covers the key aspects of the theory of stochastic processes that plays the central role in modern probability and has numerous applications in natural sciences and industry. We discuss the following topics: ways to construct and specify random processes, discrete time martingales, Levy processes and more general continuous time Markov processes, point processes. Applications to modelling random phenomena evolving in time are discussed throughout the course.
Intended learning outcomes
After completing this subject students should:
- gain an understanding of the basic concepts of the theory of stochastic processes;
- gain an understanding of the fundamental techniques used in the study of random processes;
- extend their ability to construct mathematical models for real-life situations involving uncertainty and evolving in time;
- gain the ability to pursue further studies in this and related areas.
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 November 2022