A singular stochastic differential equation driven by fractional Brownian motion

Details A singular stochastic differential equation driven by fractional Brownian motion A singular stochastic differential equation driven by fractional Brownian motion

2007-11-15

arxiv.org/abs/0711.2507v1

Mathematics

Probability

Scientific paper

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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