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.

中文翻译：

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带有随机跳的正倒向双随机微分方程和相关博弈

研究了由布朗运动和泊松过程（FBDSDEP）驱动的一类向前-向后双随机微分方程。在某些单调性假设下，通过连续法建立了FBDSDEP可测解的存在性和唯一性结果。然后讨论了针对FBDSDEP的解的连续性和可微性，具体取决于参数。此外，这些结果被应用于带有随机跳跃的后向随机双线性二次（LQ）非零和微分博弈，通过FBDSDEP的解得到开环Nash平衡点的显式形式。