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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Numerical Methods for Stochastic Differential Equations (MATH11156)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits5 ECTS Credits2.5
SummaryA 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Simulation (MATH10015)
Other requirements Students must have taken Stochastic Analysis in Finance (MATH11154)
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate familiarity with numerical schemes for simulating solutions of SDEs by answering relevant exam questions.
  2. Demonstrate conceptual understanding of the estimation of the rate of convergence of the Euler and Milstein schemes by answering relevant exam questions.
  3. Demonstrate conceptual understanding of the differences between weak and strong approximations by answering relevant exam questions.
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
KeywordsNMSDE
Contacts
Course organiserDr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk
Course secretaryMiss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk
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