Version | v2 |
Release Date | 2019-06-05 |
Primary Language | en
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Young and rough differential inclusions
release_m74u6ji5kjd7fb7dbzkpbfvzpm
by
I. Bailleul and A. Brault and L. Coutin
Abstract
We define in this work a notion of Young differential inclusion
dz_t ∈
F(z_t)dx_t,
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
dz_t ∈ F(z_t)dt + G(z_t)d X_t,
for an
α-Holder rough path 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.
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Stage
submitted
Date 2019-06-05
Version
v2
1812.06727v2
grouping other versions (eg, pre-print) and variants of this release
State is "active".
Revision:
d2bb6e35-2ef8-4eff-8ccb-42f780f031f1
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