We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.

中文翻译：

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Martingale 驱动的 BSDE、PDE 和其他相关的确定性问题

我们关注一类由 cadlag martingale 驱动的 BSDE 和相应的马尔可夫类型 BSDE，当驱动程序的随机性通过马尔可夫过程出现时就会出现。对于那些 BSDE，我们将一个确定性问题联系起来，当马尔可夫过程是布朗扩散时，它只是抛物线型 PDE。确定性问题的解旨在作为解耦温和解，它是在时间非齐次半群的帮助下制定的。