Open AccessBackward Doubly SDEs with weak Monotonicity and General Growth Generators
Author(s) -
Badreddine Mansouri,
Mostapha Abdelouahab Saouli
Publication year - 2020
Publication title -
asian journal of probability and statistics
Language(s) - English
Resource type - Journals
ISSN - 2582-0230
DOI - 10.9734/ajpas/2020/v7i230181
Subject(s) - uniqueness , monotonic function , mathematics , stochastic differential equation , square integrable function , sobolev space , geodetic datum , probabilistic logic , mathematical analysis , statistics , cartography , geography
We deal with backward doubly stochastic differential equations (BDSDEs) with a weak monotonicity and general growth generators and a square integrable terminal datum. We show the existence and uniqueness of solutions. As application, we establish the existenceand uniqueness of Sobolev solutions to some semilinear stochastic partial differential equations (SPDEs) with a general growth and a weak monotonicity generators. By probabilistic solution, we mean a solution which is representable throughout a BDSDEs.