Department of Mathematics

Stochastic Integration and Numerics

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Lecturer Dr. Andrea Barth
Room LFW E 11
Time Thu 15:15-17:00
Starts from 30.09.2010
Preliminary discussion 30.09.2010
Contact Dr. Andrea Barth
Prerequisites • Numerical Solution of Differential Equations
• Stochastic Processes I
• Numerical Analysis of Stochastic Ordinary Differential Equations
Content Stochastic partial differential equations (SPDEs) have various applications in geoscience, finance and physics. Not surprisingly the development of numerical methods for SPDEs is an increasingly active field of research. In this seminar we discuss existence and convergence of different approximation schemes for partial differential equations driven by additive or multiplicative noise and partial differential equations with stochastic differential operators.

Literature A non-exhaustive list includes the following:
• Barth, A. A finite element method for martingale-driven stochastic partial differential equations, Comm. Stoch. Anal., v.4 no.3, 2010
• Protter, P and Talay, D; The Euler scheme for Levy driven stochastic differential equations, Ann. Probab., v.25 no.1, p.393--423, 1997
• Higham, D. J.; An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Review, v.43 no.3, p.525--546, 2001
• Kovacs, M., Larsson, S. and Saedpanah, F.; Finite element approximation of the linear stochastic wave equation with additive noise, SIAM J. Numer. Anal., v.48, p.408--427, 2010
• Barth, A., Schwab, Ch. and Zollinger, N.; Multi-Level Monte Carlo Finite Element Method for elliptic PDEs with stochastic coefficients, SAM-Report, 2010

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