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.

Partner organizations

  • Technische Universität Berlin (Academic, Germany)
  • Johannes Kepler University of Linz (JKU) (Academic, Austria)
Start date 01/01/2015
End date The project is closed: 31/12/2018

​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.

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

Project leader and contact for communications
​Annika Lang, e-mail langa@chalmers.se
External partners
​Evelyn Buckwar (JKU Linz, Austria), Raphael Kruse (TU Berlin, Germany)

Funded by

  • Swedish Research Council (VR) (Public, Sweden)

Published: Thu 31 May 2018.