由Teugels Martingales驱动的前向后向随机差分方程式的可溶性 (On the solvability of forward-backward stochastic differential equations driven by Teugels Martingales)

We deal with a class of fully coupled forward-backward stochastic differential equations (FBSDE for short), driven by Teugels martingales associated with some L\'evy process. Under some assumptions on the derivatives of the coefficients, we prove the existence and uniqueness of a global solution on an arbitrarily large time interval. Moreover, we establish stability and comparison theorems for the solutions of such equations. Note that the present work extends known results by Jianfeng Zhang (Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 4, 927--940), proved for FBSDEs driven by a Brownian motion, to FBSDEs driven by general L\'evy processes.

翻译：我们处理的是一组完全相联的前向后向随机差异方程式(FBSDE,简称FBSDE),由与某些L\'evy过程相关的Teugels martingales驱动。根据对系数衍生物的一些假设,我们证明在任意的很长的时间间隔内,全球解决方案的存在和独特性。此外,我们为这些方程式的解决方案建立了稳定性并比较了理论。请注意,目前的工作延续了张建芬(Discrete Continent. Dyn. Syst. Ser. B 6(2006),第4号,第927-940)的已知结果,证明是受到布朗运动驱动的FBSDEs,与一般L\'evy过程驱动的FBSDEs。