  In this paper we study the convergence of solutions for (possibly degenerate)
stochastic differential equations driven by L\'evy processes, when the
coefficients converge in some appropriate sense. First, we prove, by means of a
superposition principle, a limit theorem of stochastic differential equations
driven by L\'evy processes. Then we apply the result to a type of nonlinear
filtering problems and obtain the convergence of the nonlinear filterings.
