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MA50251: Applied stochastic differential equations

Follow this link for further information on academic years Academic Year: 2015/6
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 25%)
  • Exam (EX 75%)
Further information on supplementary assessment Supplementary Assessment: Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions Description: Aims:
To teach those aspects of Stochastic Differential Equations which are most relevant to a general mathematical training and appropriate for students interested in stochastic modelling in the physical sciences.

Learning Outcomes:
After taking this unit, students should be able to:
* Demonstrate knowledge of stochastic differential equations and the Ito calculus.
* Use basic methods for finding solutions.
* Show awareness of the applications of these models in the physical sciences.
* Write the relevant mathematical arguments in a precise and lucid fashion.

Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing

Introduction to stochastic calculus (Brownian motion, Ito integral, Ito isometry, Fokker-Planck equation).
Additional topics will be chosen from:
* Langevin and Brownian dynamics, derivation, canonical distribution. Applications to constant-temperature molecular dynamics (heat bath).
* Metastability and exit times. Kramers' escape rate. Applications e.g., to protein conformations.
* Stochastic optimal control and Hamilton--Jacobi--Bellman equations. Applications to e.g. optimal stopping problems, stochastic target problems, portfolio selection problems, de Finetti's dividend problem.
* Stochastic PDEs. Space--time Wiener processes. Applications to modelling transition to turbulence.
* Numerical methods.
Further information on programme availabilityProgramme availability:

MA50251 is Optional on the following programmes:

Department of Mathematical Sciences
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.