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| Module Availability |
| Semester 1 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework
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25
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Written examination – 2 hours, unseen
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75
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Qualifying Condition(s)
An overall aggregate mark of 40% for the module.
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| Module Overview |
| This module introduces students to stochastic processes and its applications. |
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| Prerequisites/Co-requisites |
| MAT1028 Probability |
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| Module Aims |
| Realistic modelling of a real system very often requires the inclusion of probabilistic elements. A stochastic (as opposed to a deterministic) model will generally lead to more realistic predictions about the system. In this module we study a large class of stochastic processes, that is, probabilistic models for series of events. |
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| Learning Outcomes |
| At completion of the module the students should have a thorough understanding of the properties of stochastic processes and be able to apply this knowledge to analyse specific stochastic processes, occuring for example in finance or biology. |
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| Module Content |
| Review of basic probability theory; concept of stochastic process; random walks; properties of Markov chains: recurrence and transience, periodicity, communicating classes, irreducibility; first step analysis; Basic Limit Theorem, stationary distributions, applications. Markov processes in continuous time: derivation of the Poisson process and generalised birth and death process. |
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| Methods of Teaching/Learning |
Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading. Summary notes for the module are provided by the convener.
3 contact hours per week for 10 weeks.
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| Selected Texts/Journals |
Recommended Reading
-H.M. Taylor and S. Karlin , An Introduction to Stochastic Modelling
(rev. ed.), Academic Press, (1994).
- Murray R. Spiegel, Schaum's outline of Calculus of Finite Differences
and Difference Equations (10th printing), McGraw-Hill Trade, (1994).
Further Reading
- J.R. Norris, Markov Chains.Cambridge Series in Statistical and Probabilistic Mathematics, 1997.
- G.P. Beaumont, Introductory Applied Probability, Ellis Horwood, (1983).
- H.C. Tuckwell, Elementary Applications of Probability Theory, Chapman and Hall, (1995).
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| Last Updated |
| 3 May 2011 |
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