MA50251: Applied stochastic differential equations
[Page last updated: 05 August 2021]
Academic Year:  2021/2 
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: 

Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 

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, FokkerPlanck equation). Additional topics will be chosen from: * Langevin and Brownian dynamics, derivation, canonical distribution. Applications to constanttemperature molecular dynamics (heat bath). * Metastability and exit times. Kramers' escape rate. Applications e.g., to protein conformations. * Stochastic optimal control and HamiltonJacobiBellman equations. Applications to e.g. optimal stopping problems, stochastic target problems, portfolio selection problems, de Finetti's dividend problem. * Stochastic PDEs. Spacetime Wiener processes. Applications to modelling transition to turbulence. * Numerical methods. 
Programme availability: 
MA50251 is Optional on the following programmes:Department of Mathematical Sciences

Notes:
