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Semester 1

Applied Stochastic Differential Equations (MATH10053)







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Course Summary

Many systems include some unpredictability, and this unpredictability is typically modelled through the addition of "noise". Stochastic differential equations are a generalization of ordinary differential equations, allowing an additional noise term to be introduced. This course introduces stochastic differential equations. Starting first from their definition, through the introduction of the Ito stochastic integral, the course develops techniques for studying the properties of the stochastic processes defined by these equations, and considers the analytic solution of some simple cases. The course further introduces numerical methods which can be used to seek approximate solutions, describing how to define the numerical error in a numerical approximation of a stochastic process. The course further considers links between stochastic differential equations and partial differential equations.

Course Description

Syllabus: - Gaussian processes - Brownian motion - Ito and Stratonovich stochastic differential equations - Ito's formula - Numerical methods, including the Euler-Maruyama and Milstein schemes - Linking to partial differential equationsThe course will make use of Python.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

Additional Assessment Information

Coursework 20% , Exam 80%

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