Deep weak approximation of SDEs: a spatial approximation scheme for solving Kolmogorov equations. (English) Zbl 07714903
Summary: In this paper, we propose a new computation scheme for numerical solutions of Kolmogorov equations based on a high-order weak approximation method of stochastic differential equations and deep learning. The scheme provides a spatial approximation for solving Kolmogorov equations without the curse of dimensionality. We show numerical examples based on the proposed scheme for high-dimensional Kolmogorov equations.
Keywords:
deep learning; Kolmogorov equations; stochastic differential equations; high-order weak approximationReferences:
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