On Young Systems

R. A. Castrequini; P. J. Catuogno

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arXiv · 1412.1970

On Young Systems

R. A. Castrequini·P. J. Catuogno

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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.

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R. A. Castrequini, P. J. Catuogno. 2014-12-05. On Young Systems. https://arxiv.org/abs/1412.1970

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