Reflected backward stochastic differential equations with perturbations. (English) Zbl 1431.60046
Summary: 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, \(p\in]1,2[\), 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 \(\eta>0\) there exists an interval \([t(\eta), T]\subset [0,T]\) on which the \(L^p\)-difference between the solutions of both the perturbed and unperturbed equations is less than \(\eta\).
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
reflected backward stochastic differential equations; perturbations; \(L^p\)-stability; \(L^p\)-closenessReferences:
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