Integrability and regularity of the flow of stochastic differential equations with jumps
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 103-125
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We derive sufficient conditions for the differentiability of all orders for the
flow of stochastic differential equations with jumps and prove related
$L^p$-integrability results for all orders. Our results extend similar results
obtained by
H. Kunita
[Stochastic differential equations based on Lévy processes and
stochastic flows of diffeomorphisms, in Real and Stochastic Analysis,
Birkhäuser Boston, 2004, pp. 305–373]
for first order differentiability and rely on the Burkholder–Davis–Gundy (BDG)
inequality for time inhomogeneous Poisson random measures on $\mathbf{R}_+\times
\mathbf{R}$, for which we provide a new proof.
Keywords:
stochastic differential equations with jumps, moment bounds, Poisson random measures, stochastic flows, Markov semigroups.
@article{TVP_2020_65_1_a5,
author = {J.-Ch. Breton and N. Privault},
title = {Integrability and regularity of the flow of stochastic differential equations with jumps},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {103--125},
publisher = {mathdoc},
volume = {65},
number = {1},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a5/}
}
TY - JOUR AU - J.-Ch. Breton AU - N. Privault TI - Integrability and regularity of the flow of stochastic differential equations with jumps JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2020 SP - 103 EP - 125 VL - 65 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a5/ LA - ru ID - TVP_2020_65_1_a5 ER -
%0 Journal Article %A J.-Ch. Breton %A N. Privault %T Integrability and regularity of the flow of stochastic differential equations with jumps %J Teoriâ veroâtnostej i ee primeneniâ %D 2020 %P 103-125 %V 65 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a5/ %G ru %F TVP_2020_65_1_a5
J.-Ch. Breton; N. Privault. Integrability and regularity of the flow of stochastic differential equations with jumps. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 1, pp. 103-125. http://geodesic.mathdoc.fr/item/TVP_2020_65_1_a5/