Postgraduate Course: Numerical Methods for Stochastic Differential Equations (MATH11156)
Course Outline
| 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 |
| SCQF Credits | 5 |
ECTS Credits | 2.5 |
| Summary | A rigorous course into the theory of numerical approximations for stochastic differential equations. |
| Course description |
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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
- 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.
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Reading List
Numerical Solution of Stochastic Differential Equations
by Peter E. Kloeden and Eckhard Platen, 1999, Springer. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | NMSDE |
Contacts
| Course organiser | Dr Sotirios Sabanis
Tel: (0131 6)50 5084
Email: S.Sabanis@ed.ac.uk |
Course secretary | Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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