Reflected backward stochastic differential equations with perturbations

Jasmina Djordjević; Svetlana Janković

doi:10.3934/dcds.2018075

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2018, Volume 38, Issue 4: 1833-1848. Doi: 10.3934/dcds.2018075

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Reflected backward stochastic differential equations with perturbations

Jasmina Djordjević^, and
Svetlana Janković

Faculty of Science and Mathematics, University of Niš, Višegradska 33,18000 Niš, Serbia

* Corresponding author
* Corresponding author

Received: September 30, 2016

Revised: September 30, 2017

Published: June 2018

Supported by Grant No 174007 of MNTRS

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Abstract

This paper deals with a large class of reflected backward stochastic differential equations whose generators arbitrarily depend on a small parameter. The solutions of these equations, named the perturbed equations, are compared in the $L^p$-sense, $p∈ ]1,2[$, with the solutions of the appropriate equations of the equal type, independent of a small parameter and named the unperturbed equations. Conditions under which the solution of the unperturbed equation is $L^p$-stable are given. It is shown that for an arbitrary $η>0$ there exists an interval $[t(η), T]\subset [0,T]$ on which the $L^p$-difference between the solutions of both the perturbed and unperturbed equations is less than $η$.

Keywords:

Reflected backward stochastic differential equations,
perturbations,
L^p-stability,
L^p-closeness.

Mathematics Subject Classification: Primary: 60H35, 93E10; Secondary: 93E25.

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