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Mean reflected stochastic differential equations with jumps

Part of: Stochastic analysis Markov processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  15 July 2020

Phillippe Briand ,
Abir Ghannoum  and
Céline Labart
Phillippe Briand*
Affiliation:
Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA
Abir Ghannoum*
Affiliation:
Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA and Univ. Libanaise, LaMA-Liban
Céline Labart*
Affiliation:
Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA
*
*Postal address: Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France
**Postal address: 73000 Chambéry, France and P.O. Box 37, Tripoli, Liban
***Postal address: 73000Chambéry, France. Email address: [email protected]
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Abstract

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.

Keywords

Reflected stochastic differential equationjumpsparticle systems

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 65C35: Stochastic particle methods 60J75: Jump processes
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 2 , June 2020 , pp. 523 - 562
Copyright
© Applied Probability Trust 2020

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