Wong-Zakai approximation of density functions

Yuzuru Inahama

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arXiv · 2304.01449

Wong-Zakai approximation of density functions

Yuzuru Inahama

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Abstract

In this paper we prove the Wong-Zakai approximation of probability density functions of solutions at a fixed time of rough differential equations driven by fractional Brownian rough path with Hurst parameter $H$ $(1/4 <H \leq 1/2)$. Besides rough path theory, we use Hu-Watanabe's approximation theorem in the framework of Watanabe's distributional Malliavin calculus. When $H=1/2$, the random rough differential equations coincide with the corresponding Stratonovich-type stochastic differential equations. Even for that case, our main result seems new.

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Yuzuru Inahama. 2023-04-04. Wong-Zakai approximation of density functions. https://arxiv.org/abs/2304.01449

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