A weak approximation for Bismut's formula: An algorithmic differentiation method

The paper provides a novel algorithmic differentiation method by constructing a weak approximation for Bismut's formula. A new operator splitting method based on Gaussian Kusuoka-approximation is introduced for an enlarged semigroup describing differentiation of diffusion semigroup. The effectiveness of the new algorithmic differentiation is checked through numerical examples. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

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The paper presents a novel algorithmic differentiation method using a weak approximation of the Bismut formula. It introduces a new operator splitting method based on Gaussian Kusuoka approximation for an enlarged semigroup that describes the differentiation of diffusion semigroup. The effectiveness of the new algorithmic differentiation is demonstrated through numerical examples.