Approximation and simulation of Lévy-driven SPDE

​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.

Keywords: stochastic partial differential equations, numerical approximation, stochastic simulation

• Annika Lang

  Professor, Mathematical Sciences

  My research interests include numerical analysis of stochastic partial differential equations and regularity and simulation of random fields. I am head of unit within the division of applied...
• Adam Andersson

  Guest researcher, Mathematical Sciences

  My current research concerns applications of deep learning to numerical analysis. Deep learning has previously revolutionalized computer vision and natural language processing. A similar trend has...
• David Bolin

  Associate professor, Mathematical Sciences

  My primary research areas are spatial statistics, spatio-temporal modeling, and computationally efficient inference methods for analysis of large data sets.
• Stig Larsson

  Professor, Mathematical Sciences

  The research of Stig Larsson is concerned with the numerical solution of partial differential equations, in particular finite element methods. Currently his main interest is stochastic partial...
• Andreas Petersson

  Researcher, Mathematical Sciences

  I completed my dissertation in mathetmatical statistics 2019 at Chalmers with the thesis title "Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and...