A note on functional limit theorems for compound Cox processes
Probability
2016-06-29 v1
Abstract
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 L{\'e}vy 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 L{\'e}vy processes with variance-mean mixed normal distributions, in particular, to stable L{\'e}vy processes, generalized hyperbolic and generalized variance-gamma L{\'e}vy processes.
Cite
@article{arxiv.1507.02534,
title = {A note on functional limit theorems for compound Cox processes},
author = {V. Yu. Korolev and A. V. Chertok and A. Yu. Korchagin and E. V. Kossova and A. I. Zeifman},
journal= {arXiv preprint arXiv:1507.02534},
year = {2016}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1410.1900