Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion

David Nualart and Bruno Saussereau

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 391-409

Abstract: We prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H>0.5. The result is based on the Fréchet differentiability with respect to the input function for deterministic differential equations driven by Hölder continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, under a suitable nondegeneracy condition.

Keywords: Stochastic; differential; equation; Malliavin; calculus; Fractional; Brownian; motion (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (20)

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