Quasi-invariant theorem on the Gaussian path space

Qinpin Chen; Jian Sun; Bo Wu

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arXiv · 2311.11358

Quasi-invariant theorem on the Gaussian path space

Qinpin Chen·Jian Sun·Bo Wu

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Abstract

In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the case of the fractional Brownian motion. As applications, we will establish the integration by parts formula and Bismut-Elworthy-Li formula on the Gaussian path space, and by which some logarithmic Sobolev inequalities will be presented. Moreover, we will also provides some applications in the field of financial mathematics.

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Qinpin Chen, Jian Sun, Bo Wu. 2023-11-19. Quasi-invariant theorem on the Gaussian path space. https://arxiv.org/abs/2311.11358

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