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arXiv · 2102.02693

Skorohod and Stratonovich integrals for controlled processes

Jian Song·Samy Tindel
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Abstract

Given a continuous Gaussian process $x$ which gives rise to a $p$-geometric rough path for $p\in (2,3)$, and a general continuous process $y$ controlled by $x$, under proper conditions we establish the relationship between the Skorohod integral $\int_0^t y_s {\mathrm{d}}^\diamond x_s$ and the Stratonovich integral $\int_0^t y_s {\mathrm{d}} {\mathbf x}_s$. Our strategy is to employ the tools from rough paths theory and Malliavin calculus to analyze discrete sums of the integrals.

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Jian Song, Samy Tindel. 2021-02-04. Skorohod and Stratonovich integrals for controlled processes. https://arxiv.org/abs/2102.02693

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