A singular stochastic differential equation driven by fractional Brownian motion

2007/11/15 by Yaozhong Hu, David Nualart, Hu, Yaozhong +3
Mathematics · #60H05 #60H07 #60H10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60H05 #msc:60H07 #msc:60H10

paper · pdf · doi:10.48550/arxiv.0711.2507

arxiv created 2007/11/15 · arxiv updated 2009/12/01

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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