Some differential systems driven by a fBm with Hurst parameter greater than 1/4

Details Some differential systems driven by a fBm with Hurst parameter greater than 1/4 Some differential systems driven by a fBm with Hurst parameter greater than 1/4

2009-01-14

arxiv.org/abs/0901.2010v1

Mathematics

Probability

32 pages

Scientific paper

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with H\"older regularity greater than 1/4. After recalling how to treat the case of ordinary stochastic differential equations, we mainly focus on the case of delay equations. A careful analysis is then performed in order to show that a fractional Brownian motion with Hurst parameter H>1/4 fulfills the assumptions of our abstract theorems.

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