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 Academic Year: | 2016/7 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Masters UG & PG (FHEQ level 7) |
| Period: |
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| Assessment Summary: | CW 25%, EX 75% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | |
| 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. Skills: Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing Content: 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. |
| Programme availability: |
MA50251 is Optional on the following programmes:Department of Mathematical Sciences
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Notes:
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