Necessary and sufficient conditions for the convergence of semimartingales to processes with conditionally independent increments (Q1058223)

A notion of stably weak convergence different from the one considered by \textit{D. Aldous} [Weak convergence of stochastic processes for processes viewed in the Strasbourg manner. Preprint (1978)] and \textit{I. S. Helland} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 52, 251-265 (1980; Zbl 0411.60037)] is introduced. The main result states necessary and sufficient conditions in terms of predictable characteristics for stably weak convergence of a sequence of semimartingales to the quasi-left continuous process with conditionally independent increments.