Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-6,
author = {W. Szczotka and P. \.Zebrowski},
title = {On fully coupled continuous time random walks},
journal = {Applicationes Mathematicae},
volume = {39},
year = {2012},
pages = {87-102},
zbl = {1237.60038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-6}
}
W. Szczotka; P. Żebrowski. On fully coupled continuous time random walks. Applicationes Mathematicae, Tome 39 (2012) pp. 87-102. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am39-1-6/