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Numerical solution of kinetic SPDEs via stochastic Magnus expansion

Author

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  • Kamm, Kevin
  • Pagliarani, Stefano
  • Pascucci, Andrea

Abstract

In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space only by utilizing finite difference methods and vectorize the resulting equation exploiting its sparsity.

Suggested Citation

  • Kamm, Kevin & Pagliarani, Stefano & Pascucci, Andrea, 2023. "Numerical solution of kinetic SPDEs via stochastic Magnus expansion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 189-208.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:189-208
    DOI: 10.1016/j.matcom.2022.12.029
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    References listed on IDEAS

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    1. Kevin Kamm & Michelle Muniz, 2022. "A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups," Papers 2205.15699, arXiv.org.
    2. Michael B. Giles & Christoph Reisinger, 2012. "Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance," Papers 1204.1442, arXiv.org.
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