Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes (Q2680327)
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scientific article
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| English | Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes |
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Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes (English)
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28 December 2022
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Nonlinear partial differential equations of Kolmogorov type appear in physical, engineering and finance applications. The authors present an approach to solve equations of this type using a deep network trained from the samples of discretized stochastic differential equation. Accuracy and computational complexity issues are studied.
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Kolmogorov equation
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numerical analysis
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Milstein discretization
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Euler-Maruyama approximation
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Leimkuhler-Matthews approximation
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deep learning
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