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arxiv: 0801.3314 · v1 · submitted 2008-01-22 · 🧮 math.PR

Occupation densities for certain processes related to fractional Brownian motion

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keywords brownianexistencefractionalintegrablemotionoccupationprocessessquare
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In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter $H>\frac 12$. The proof of these results uses a general criterion for the existence of a square integrable local time, which is based on the techniques of Malliavin calculus.

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