  In this paper we focus on the so called identification problem for a backward
SDE driven by a continuous local martingale and a possibly non
quasi-left-continuous random measure. Supposing that a solution (Y, Z, U) of a
backward SDE is such that $Y(t) = v(t, X(t))$ where X is an underlying process
and v is a deterministic function, solving the identification problem consists
in determining Z and U in term of v. We study the over-mentioned identification
problem under various sets of assumptions and we provide a family of examples
including the case when X is a non-semimartingale jump process solution of an
SDE with singular coefficients.

Probability