Before revision:  This allows us to connect the previous control problem to a  quadratic BSDE with jumps that is new to the literature , in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter.
After revision:  This allows us to connect the previous control problem to a new type of quadratic BSDE with jumps that is new to the literature , in which the driver term has non-standard structures and carries the conditional filter as an infinite-dimensional parameter.