2018/12/17 by Ismaël Bailleul, Bailleul, I., Brault, A. +1
Mathematics · #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.1812.06727
We define in this work a notion of Young differential inclusion dzt ∈ F(zt)dxt, for an α-Holder control x, with α>1/2, and give an existence result for such a differential system. As a by-product of our proof, we show that a bounded, compact-valued, γ-Hölder continuous set-valued map on the interval [0,1] has a selection with finite p-variation, for p>1/γ. We also give a notion of solution to the rough differential inclusion dzt ∈ F(zt)dt + G(zt)d\bf Xt, for an α-Holder rough path \bf X with α∈ ((1)/(3),(1)/(2)], a set-valued map F and a single-valued one form G. Then, we prove the existence of a solution to the inclusion when F is bounded and lower semi-continuous with compact values, or upper semi-continuous with compact and convex values.