Malliavin Calculus for Fractional Delay Equations

Jorge A. León () and Samy Tindel ()
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Jorge A. León: CINVESTAV-IPN
Samy Tindel: Institut Élie Cartan Nancy

Journal of Theoretical Probability, 2012, vol. 25, issue 3, 854-889

Abstract: Abstract In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a Hölder continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2 has a C ∞-density. To this purpose, we use Malliavin calculus based on the Fréchet differentiability in the directions of the reproducing kernel Hilbert space associated with fBm.

Keywords: Delay equation; Young integration; Fractional Brownian motion; Malliavin calculus; 60H10; 60H05; 60H07 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0349-4

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