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On Young Systems (1412.1970v1)
Published 5 Dec 2014 in math.AP
Abstract: In this article, we study differential equations driven by continuous paths with with bounded $p$-variation for $1 \leq p< 2$ (Young systems). The most important class of examples of theses equations is given by stochastic differential equations driven by fractional Brownian motion with Hurst index $H >\frac{1}{2}$. We give a formula type It^o-Kunita-Ventzel and a substitution formula adapted to Young integral. It allows us to give necessary conditions for existence of conserved quantities and symmetries of Young systems. We give a formula for the composition of two flows associated to Young sistems and study the Cauchy problem for Young partial differential equations.