Mean reflected stochastic differential equations with jumps

In this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These reflected SDEs have been approximated by Briand et al. (2016) using a numerical scheme based on particles systems,...

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Bibliographic Details
Published inAdvances in applied probability Vol. 52; no. 2; pp. 523 - 562
Main Authors Briand, Phillippe, Ghannoum, Abir, Labart, Céline
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2020
Applied Probability Trust
Subjects
Approximation
Differential equations
Mathematics
Original Article
Original Articles
Probability
Random variables
60J75
Reflected stochastic differential equation
jumps
60H10
65C35
particle systems
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Summary:In this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These reflected SDEs have been approximated by Briand et al. (2016) using a numerical scheme based on particles systems, when no jumps occur. The main contribution of this paper is to prove the existence and the uniqueness of the solutions to this kind of reflected SDE with jumps and to generalize the results obtained by Briand et al. (2016) to this context.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2020.11