- Academic Registry
Programme & Unit Catalogues

MA50251: Applied stochastic differential equations

[Page last updated: 03 August 2022]

Academic Year: 2022/23
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)
Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
  • Coursework (CW 25%)
  • Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
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.

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.

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


  • This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
  • Programmes and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.