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Z Brzezniak & T Zastawniak, Basic Stochastic Processes, Springer. T Mikosch, Elementary stochastic calculus with finance in view, World Scientific. G R Grimmett & D R Stirzaker, Probability and random processes, OUP.Ĭ W Gardiner, Handbook of stochastic methods, Springer. Coursework and examinations will be marked and returned in accordance with this policy. Examples include: geometric Brownian motion Ornstein-Uhlenbeck processĬlosed/in-person Exam (Centrally scheduled)Ĭurrent Department policy on feedback is available in the undergraduate student handbook. Stochastic differential equations and Ito’s calculus. Give examples of applications of stochastic processes įormulate and analyse Markov models in continuous time Ĭalculate (conditional) probabilities of events and expectations of variables described by simple Markov processes like the Poisson process or the Wiener process ĭetermine transition rates stationary distributions of birth-death processes ĭiscuss the properties of the Wiener process ĭefine the Ito stochastic integral and give its important properties Īpply Ito's Lemma to find solutions of certain stochastic differential equations ĭiscrete state-space: Markov jump processesĬontinuous state-space, stochastic calculus To provide a range of mathematical techniques and approximations that can be used to make analytic predictions from stochastic models Īt the end of the module the student should be able to:Īppreciate the uses for stochastic models, their characteristics and limitations Įxplain the concept of continuous-time stochastic processes and the Markov property.To demonstrate the circumstances in which continuous-time stochastic models give results that are different to those from deterministic models that neglect the random effects.To introduce students to a range of mathematical models that take account of the stochastic (random) fluctuations that are always present in the real world.
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Pre-requisites for Natural Sciences students: must have taken Statistics Option MAT00033I.
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