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Minimal solution of irregular barrier reflected BDSDEs with left continuous and stochastic linear growth generators
by Mostapha Abdelouahab Saouli  

Vol. 18 No. 2 (2023) P.185~P.224
DOI: https://doi.org/10.21915/BIMAS.2023203
  10.21915/BIMAS.2023203

ABSTRACT

In this paper, we deal with reflected backward doubly stochastic differential equations (RBDSDEs in short) with one rcll reflecting barrier when the coefficient $f$ satisfies a stochastic Lipschitz condition, via penalization method we prove the existence and uniqueness of solutions. The comparison theorem is also established. Via an inf-convolution approximation and comparison theorem, we show the existence of a minimal solution to the RBDSDE under continuous and stochastic linear growth condition, also we provide a minimal solution to RBDSDE with left continuous and stochastic linear growth condition.


KEYWORDS
RBDSDE, penalization method, stochastic linear growth, stochastic Lipschitz-continuous

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60H10, 60H05

MILESTONES

Received: 2022-12-25
Revised :
Accepted:


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