A Skorohod measurable universal functional representation of solutions to semimartingale SDEs

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Hauptverfasser:	Przybyłowicz, Paweł, Schwarz, Verena, Steinicke, Alexander, Szölgyenyi, Michaela
Format:	Preprint
Veröffentlicht:	2022
Schlagworte:	Probability 60H10, 60H07, 60G51
Online-Zugang:	Acceder al recurso
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author	Przybyłowicz, Paweł Schwarz, Verena Steinicke, Alexander Szölgyenyi, Michaela
author_facet	Przybyłowicz, Paweł Schwarz, Verena Steinicke, Alexander Szölgyenyi, Michaela
contents	In this paper we show the existence of a universal Skorohod measurable functional representation for a large class of semimartingale-driven stochastic differential equations. For this we prove that paths of the strong solutions of stochastic differential equations can be written as measurable functions of the paths of their driving processes into the space of all càdlàg functions equipped with the Borel sigma-field generated by all open sets with respect to the Skorohod metric. This result can be applied to calculate Malliavin derivatives for SDEs driven by pure-jump Lévy processes with drift.
format	Preprint
id	arxiv_https___arxiv_org_abs_2201_06278
institution	arXiv
publishDate	2022
record_format	arxiv
spellingShingle	A Skorohod measurable universal functional representation of solutions to semimartingale SDEs Przybyłowicz, Paweł Schwarz, Verena Steinicke, Alexander Szölgyenyi, Michaela Probability 60H10, 60H07, 60G51 In this paper we show the existence of a universal Skorohod measurable functional representation for a large class of semimartingale-driven stochastic differential equations. For this we prove that paths of the strong solutions of stochastic differential equations can be written as measurable functions of the paths of their driving processes into the space of all càdlàg functions equipped with the Borel sigma-field generated by all open sets with respect to the Skorohod metric. This result can be applied to calculate Malliavin derivatives for SDEs driven by pure-jump Lévy processes with drift.
title	A Skorohod measurable universal functional representation of solutions to semimartingale SDEs
topic	Probability 60H10, 60H07, 60G51
url	https://arxiv.org/abs/2201.06278

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