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arXiv · 0711.2507

A singular stochastic differential equation driven by fractional Brownian motion

Yaozhong Hu·David Nualart·Xiaoming Song
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Abstract

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time $t>0$.

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Yaozhong Hu, David Nualart, Xiaoming Song. 2007-11-15. A singular stochastic differential equation driven by fractional Brownian motion. https://arxiv.org/abs/0711.2507

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