Postgraduate Course: Numerical Methods for Stochastic Differential Equations (MATH11156)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||A rigorous course into the theory of numerical approximations for stochastic differential equations.
Preliminaries: Burkholder-Davis-Gundy inequality and Gronwall' s lemma. Strong and weak approximations of solutions to SDEs.
Euler's approximations and Milstein's scheme.
Order of accuracy of numerical approximations.
Higher order schemes, accelerated convergence.
Weak approximations of SDEs via numerical solutions of PDEs.
Entry Requirements (not applicable to Visiting Students)
|Prohibited Combinations|| Students MUST NOT also be taking
||Other requirements|| Students must have taken Stochastic Analysis in Finance (MATH11154)
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- Demonstrate familiarity with numerical schemes for simulating solutions of SDEs by answering relevant exam questions.
- Demonstrate conceptual understanding of the estimation of the rate of convergence of the Euler and Milstein schemes by answering relevant exam questions.
- Demonstrate conceptual understanding of the differences between weak and strong approximations by answering relevant exam questions.
|Numerical Solution of Stochastic Differential Equations|
by Peter E. Kloeden and Eckhard Platen, 1999, Springer.
|Graduate Attributes and Skills
|Course organiser||Dr Lukasz Szpruch
Tel: (0131 6)50 5742
|Course secretary||Miss Sarah McDonald
Tel: (0131 6)50 5043