Before revision: We extend the monotone stability approach for backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure , which can be of infinite activity and time-inhomogeneous with non-deterministic  compensator.
After revision: We extend the monotone stability approach to backward stochastic differential equations (BSDEs) that are jointly driven by a Brownian motion and a random measure , which can be of infinite activity and time-inhomogeneous with non-deterministic compensator.