Deep Weak Approximation of SDEs: A Spatial Approximation Scheme for Solving Kolmogorov Equations

Riu Naito; Toshihiro Yamada

doi:10.1142/S0219876221420147

Deep Weak Approximation of SDEs: A Spatial Approximation Scheme for Solving Kolmogorov Equations

Riu Naito, Toshihiro Yamada^*

^*この論文の責任著者

経済学科　経済学

研究成果: ジャーナルへの寄稿 › 学術論文 › 査読

3 被引用数 (Scopus)

抄録

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.

本文言語	英語
論文番号	2142014
ジャーナル	International Journal of Computational Methods
巻	19
号	8
DOI	https://doi.org/10.1142/S0219876221420147
出版ステータス	出版済み - 2022/10/01

ASJC Scopus 主題領域

コンピュータサイエンス（その他）
計算数学

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10.1142/S0219876221420147

引用スタイル

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abstract = "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.",

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Y1 - 2022/10/1

N2 - 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.

AB - 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.

KW - Deep learning

KW - Kolmogorov equations

KW - high-order weak approximation

KW - stochastic differential equations

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Deep Weak Approximation of SDEs: A Spatial Approximation Scheme for Solving Kolmogorov Equations

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