@article{EJP965,
author = {Sana Louhichi and Emmanuel Rio},
title = {Functional Convergence to Stable Lévy Motions for Iterated Random Lipschitz Mappings},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {16},
year = {2011},
keywords = {Partial sums processes. Skorohod topologies. Functional limit theorem. Association. Tightness. Ottaviani inequality. Stochastically monotone Markov chains. Iterated random Lipschitz mappings.},
abstract = {It is known that, in the dependent case, partial sums processes which are elements of $D([0,1])$ (the space of right-continuous functions on $[0,1]$ with left limits) do not always converge weakly in the $J_1$-topology sense. The purpose of our paper is to study this convergence in $D([0,1])$ equipped with the $M_1$-topology, which is weaker than the $J_1$ one. We prove that if the jumps of the partial sum process are associated then a functional limit theorem holds in $D([0,1])$ equipped with the $M_1$-topology, as soon as the convergence of the finite-dimensional distributions holds. We apply our result to some stochastically monotone Markov chains arising from the family of iterated Lipschitz models.},
pages = {no. 89, 2452-2480},
issn = {1083-6489},
doi = {10.1214/EJP.v16-965},
url = {http://ejp.ejpecp.org/article/view/965}}