Linear Stochastic Differential Equations Driven by a Fractional Brownian Motion with Hurst Parameter less than 1/2

2006/03/28 by Jorge A. Leon, Leon, Jorge A., Jaime San Martin +1
Mathematics · #60H05 #60H07 #60H20 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:60H05 #msc:60H07 #msc:60H20 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0603636

arxiv created 2006/03/28 · arxiv updated 2009/12/01

Abstract

In this paper we use the chaos decomposition approach to establish the existence of a unique continuous solution to linear fractional differential equations of the Skorohod type. Here the coefficients are deterministic, the inital condition is anticipating and the underlying fractional Brownian motion has Hurst parameter less than 1/2. We provide an explicit expression for the chaos decomposition of the solution in order to show our results.

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