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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

### Annika Lang (contact)

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Adam Andersson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### David Bolin

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Andreas Petersson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

## Collaborations

### Johannes Kepler University of Linz (JKU)

Linz, Austria

### Technische Universität Berlin

Berlin, Germany

## Funding

### Swedish Research Council (VR)

Project ID: 2014-3995

Funding Chalmers participation during 2015–2018

## Publications

**2023**

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

**Journal article**