CTRW-limits in the the Skorokhod topology and FPK equations associated with SDEs driven by CTRW-limit processes

In this paper we study conditions under which a wide class of continuous time random walk stochastic processes have limits in the J1- and M1-topologies of the Skorokhod space of c`adl`ag processes. The approach used for the proof is based on the theory of convergence of composite stochastic processes developed by Silvestrov in the 1970th. Stochastic differential equations driven by such limits are introduced. Fokker-Planck-Kolmogorov equations associated with the corresponding SDEs driven by CTRW-limits are established.