Smoothing effect of rough differential equations driven by fractional Brownian motions

Fabrice Baudoin; Cheng Ouyang; Xuejing Zhang

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arXiv · 1304.4838

Smoothing effect of rough differential equations driven by fractional Brownian motions

Fabrice Baudoin·Cheng Ouyang·Xuejing Zhang

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Abstract

In this work we study the smoothing effect of rough differential equations driven by a fractional Brownian motion with parameter $H>1/4$. The regularization estimates we obtain generalize to the fractional Brownian motion previous results by Kusuoka and Stroock and can be seen as a quantitative version of the existence of smooth densities under H\"ormander's type conditions.

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Fabrice Baudoin, Cheng Ouyang, Xuejing Zhang. 2013-04-17. Smoothing effect of rough differential equations driven by fractional Brownian motions. https://arxiv.org/abs/1304.4838

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