
Digital Library of the
European Council for Modelling and Simulation 
Title: 
On
Convergence Of Random Walks Having Jumps With Finite Variances To Stable Levy
Processes 
Authors: 
Victor Korolev,
Vladimir Bening, Lilya Zaks, Alexander Zeifman 
Published in: 
(2013).ECMS 2013 Proceedings edited
by: W. Rekdalsbakken, R. T. Bye, H. Zhang European Council for Modeling
and Simulation. doi:10.7148/2013 ISBN:
9780956494467 27^{th}
European Conference on Modelling and Simulation, Aalesund, Norway, May 27^{th} –
30^{th}, 2013 
Citation
format: 
Victor
Korolev, Vladimir Bening,
Lilya Zaks, Alexander Zeifman (2013). On Convergence Of Random Walks Having
Jumps With Finite Variances To Stable Levy Processes,
ECMS 2013 Proceedings edited by: W. Rekdalsbakken, R. T. Bye, H. Zhang, European Council for Modeling
and Simulation. doi:10.7148/20130601 
DOI: 
http://dx.doi.org/10.7148/20130601 
Abstract: 
A
functional limit theorem is proved establishing weak convergence of random
walks generated by compound doubly stochastic Poisson processes to Levy
processes in the Skorokhod space. As corollaries,
theorems are proved on convergence of random walks with jumps having finite
variances to Levy processes with mixed normal distributions, in particular,
to stable Levy processes. Statistical analysis of the traffic in information
flows in modern computational and telecommunication systems sometimes shows
that this characteristics possesses the property of
selfsimilarity. In applied probability this property is
usually modeled by Levy processes. This communication gives some
theoretical grounds to this convention. 
Full
text: 