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Weak convergence for semi-linear SPDEs.
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mardi, 31 janvier 2017
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Faculté des sciences -
Section de mathématiques
Joint work with Arnulf Jentzen, Ryan Kurniawan, and Timo Welti.
In numerical analysis for stochastic differential equations, a general rule of thumb is that the optimal weak convergence rate of a numerical scheme is twice the optimal strong convergence rate. However, for SPDEs the optimal weak convergence rate is difficult to establish theoretically. Recently, progress was been made by Jentzen, Kurniawan and Welti for semi-linear SPDEs using the so-called mild Itô formula. We consider this approach for wave equations.
In numerical analysis for stochastic differential equations, a general rule of thumb is that the optimal weak convergence rate of a numerical scheme is twice the optimal strong convergence rate. However, for SPDEs the optimal weak convergence rate is difficult to establish theoretically. Recently, progress was been made by Jentzen, Kurniawan and Welti for semi-linear SPDEs using the so-called mild Itô formula. We consider this approach for wave equations.
Collection
Workshop on Multiscale methods for stochastic dynamics
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Stochastic parameterizations of deterministic dynamical systems: Theory, applications and challenges
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Ergodic Stochastic Differential Equations and Sampling: A numerical analysis perspective
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Weak convergence for semi-linear SPDEs.
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On stochastic numerical methods for the approximative pricing of financial derivatives.
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Mean-square stability analysis of SPDE approximations.
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Accelerated dynamics and transition state theory.
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Long-time homogenization of the wave equation.
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