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Forward‐backward doubly stochastic differential equations with random jumps and related games
Author(s) -
Zhu Qingfeng,
Shi Yufeng,
Teng Bin
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2344
Subject(s) - mathematics , stochastic differential equation , differentiable function , uniqueness , monotonic function , continuation , brownian motion , differential game , differential (mechanical device) , nash equilibrium , mathematical analysis , type (biology) , mathematical economics , mathematical optimization , computer science , physics , ecology , statistics , biology , thermodynamics , programming language
A type of forward‐backward doubly stochastic differential equations driven by Brownian motions and the Poisson process (FBDSDEP) is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions of FBDSDEP are established via a method of continuation. Then the continuity and differentiability of the solutions to FBDSDEP depending on parameters is discussed. Furthermore, these results were applied to backward doubly stochastic linear quadratic (LQ) nonzero sum differential games with random jumps to get the explicit form of the open‐loop Nash equilibrium point by the solution of the FBDSDEP.