Approximation and simulation of Lévy-driven SPDE

Research Project, 2015 – 2018

​Numerical analysis of stochastic partial differential equations is a quite young and very active area of research. Since analytical solutions of these equations are only rarely available, approximation of sample paths, moments, or probabilities is necessary. The quantity of interest depends on the type of application, e.g., finance, engineering, or filtering. The goal of the project is to answer some current open questions in the research area with methods from stochastic analysis, numerical analysis, and mathematical statistics. The research questions are related to different definitions of consistency of approximation schemes, the Lax equivalence theorem, weak convergence results using Malliavin calculus, construction of efficient algorithms for random fields, statistical properties of multilevel Monte Carlo algorithms, and mean-square stability regions.

Participants

Collaborations

Funding

Publications

Approximation of SPDE covariance operators by finite elements: a semigroup approach

Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces

Drift-preserving numerical integrators for stochastic Hamiltonian systems

Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise

Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs

Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

More information

Project Web Page at Chalmers

http://www.chalmers.se/en/projects/Pages/A...

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