In this paper, we study a system of second order integro-partial differential equations with interconnected obstacles with non-local terms, related to an optimal switching problem with the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution which is unique in the class of functions with polynomial growth. In our study, the main tool is the associated of reflected backward stochastic differential equations with jumps with interconnected obstacles for which we show the existence of a unique Markovian solution.

中文翻译：

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具有非局部性且无单调性的障碍的积分-偏微分方程组的粘滞解

在本文中，我们研究了具有非局部项的相互连接障碍物的二阶积分-偏微分方程组，该系统与具有跳跃扩散模型的最优切换问题有关。摆脱了关于跳跃分量的生成器上的单调性条件，我们构造了一个连续的粘度解，该解在具有多项式增长的函数类别中是唯一的。在我们的研究中，主要工具是反射的倒向随机微分方程与具有互连障碍物的跳跃相关联，为此我们展示了唯一的马尔可夫解的存在。