V. Yu. Korolev, L. M. Zaks, A. I. Zeifman, “On convergence of random walks generated by compound Cox processes to Levy processes”, Inform. Primen., 2013, Volume 7, Issue 2,Pages <nobr>84

On convergence of random walks generated by compound Cox processes to Levy processes

V. Yu. Korolev^ab, L. M. Zaks^c, A. I. Zeifman^db

^a Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
^b IPI RAN
^c Department of Modeling and Mathematical Statistics, Alpha-Bank
^d Vologda State Pedagogical University

Abstract: A functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes to Lévy processes in the Skorokhod space. As corollaries, theorems on convergence of random walks with jumps having finite variances to Lévy processes with mixed normal distributions, in particular, to stable Lévy processes have been proved.

Keywords: stable distribution; Lévy process; stable Lévy process; compound doubly stochastic Poisson process (compound Cox process); Skorokhod space; transfer theorem.