Mini-course on numerical methods for SDEs
30 August - 02 September, 2016

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The mini-course is designed to give an accessible introduction to numerical discretisation of stochastic differential equations (SDEs). Prerequisites will be kept to a minimum. We assume only a basic competence in calculus (including ordinary differential equations) and probability. Some familiarity with fundamental concepts from numerical analysis is also desirable, but not absolutely necessary. We will mention some open research problems and discuss applications in molecular dynamics and financial engineering.

Basics of stochastic processes and SDEs
Numerical methods for SDEs -- the mean-square sense
Numerical methods for SDEs -- the weak sense
Basics of the Monte Carlo technique and variance reduction
Computing ergodic limits
Stochastic geometric integration
Applications in molecular dynamics and finance

Handout of the mini-course.




  Tuesday August 30, 2016
10:15-12:00 (N430) Lecture: Revision of probability; Stochastic processes; Brownian motion
12:00-13:00 Lunch
13:15-15:00 (MA356) Lecture: Stochastic integrals; SDEs; Stochastic numerics
  Wednesday August 31, 2016
11:15-12:00 (MA141) Computer Lab
12:00-13:00 Lunch
13:15-16:00 (MC413) Lecture: MS approximation; A.s convergence; Weak error; Monte-Carlo
  Thursday September 01, 2016
11:15-12:00 (MA141) Computer Lab
12:00-13:00 Lunch
13:15-16:00 (MA356) Lecture: Computing ergodic limits; Stochastic geometric integration
  Friday September 02, 2016
10:15-12:00 (MA136) Consultation
12:00-13:00 Lunch


Practical Informations

List of Participants (last update: 18.06.16)