Financial/Actuarial Mathematics Seminar

In case of one spatial variable, we consider the question of the weakest possible topology, which provides convergence of the solutions. Convergence of solutions of initial-boundary value problems is equivalent to weak convergence of corresponding diffusion processes. In general, the infinitesimal generator of limiting processes need not to be a classical second order elliptic differential operator. Continuous Markov processes corresponding to the generalized second order differential operators introduced by W. Feller can appear as limiting processes. We provide necessary and sufficient conditions that guarantee the convergence of solutions of initial-boundary value problems for parabolic equations.