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Mean‐field backward stochastic differential equations driven by G ‐Brownian motion and related partial differential equations
Author(s) -
Sun Shengqiu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6573
Subject(s) - mathematics , stochastic differential equation , stochastic partial differential equation , mathematical analysis , uniqueness , brownian motion , differential equation , mean field theory , statistics , physics , quantum mechanics
In this paper, we study mean‐field backward stochastic differential equations driven by G ‐Brownian motion ( G ‐BSDEs). We first obtain the existence and uniqueness theorem of these equations. In fact, we can obtain local solutions by constructing Picard contraction mapping for Y term on small interval, and the global solution can be obtained through backward iteration of local solutions. Then, a comparison theorem for this type of mean‐field G ‐BSDE is derived. Furthermore, we establish the connection of this mean‐field G ‐BSDE and a nonlocal partial differential equation. Finally, we give an application of mean‐field G ‐BSDE in stochastic differential utility model.