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Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation

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  • Flandoli, Franco
  • Luo, Dejun
  • Ricci, Cristiano

Abstract

Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are considered. The aim is to numerically compute the expected values and probabilities associated to their solutions, by solving the corresponding Kolmogorov equations, with a partial use of Monte Carlo strategy - precisely, using Monte Carlo only for the linear part of the SDE. The basic idea was presented in [16], but here we strongly improve the numerical results by means of a shift of the auxiliary Gaussian process. For relatively simple nonlinearities, we have good results in dimension of the order of 100.

Suggested Citation

  • Flandoli, Franco & Luo, Dejun & Ricci, Cristiano, 2023. "Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s009630032200594x
    DOI: 10.1016/j.amc.2022.127520
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    References listed on IDEAS

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    1. Weinan E & Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse, 2021. "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-31, December.
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