Some Functional Limit Theorems for Compound Cox Processes

摘要

An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Levy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Levy processes with variance-mean mixed normal distributions, in particular, to stable Levy processes.