Geodesic
Anticipated backward doubly stochastic differential equations driven by Teugels martingales with or without reflecting barrier
Daghestan Electronic Mathematical Reports, Tome 13 (2020), pp. 1-21

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We are interested in this paper on reflected anticipated backward doubly stochastic differential equations (RABDSDEs) driven by teugels martingales associated with Levy process. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem where the coefficients of these BDSDEs depend on the future and present value of the solution $(Y, Z)$. We also show the comparison theorem for a special class of RABDSDEs under some slight stronger conditions. The novelty of our result lies in the fact that we allow the time interval to be infinite.
Keywords: anticipated backward doubly stochastic differential equations, random Levy measure, comparison theorem, predictable representation, Teugels martingales. 
@article{DEMR_2020_13_a0,
     author = {M. Saouli and B. Mansouri},
     title = {Anticipated backward doubly stochastic differential equations driven by {Teugels} martingales with or without reflecting barrier},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {1--21},
     publisher = {mathdoc},
     volume = {13},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2020_13_a0/}
}
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M. Saouli; B. Mansouri. Anticipated backward doubly stochastic differential equations driven by Teugels martingales with or without reflecting barrier. Daghestan Electronic Mathematical Reports, Tome 13 (2020), pp. 1-21. http://geodesic.mathdoc.fr/item/DEMR_2020_13_a0/