This paper is concerned with the almost everywhere convergence of martingales indexed by countable filtering sets. It is shown that the convergence is a consequence of the maximal inequality as it is in the classical case. It also contains some results about the law of large numbers when the index belongs to a sector and an optimal condition assuring the almost everywhere convergence of martingales in these sectors.
Publié le : 1977-12-14
Classification:
Filtering sets,
martingales,
almost everywhere convergence,
law of large numbers,
sectors,
stochastic convexity,
60G45,
60F15,
60G50
@article{1176995658,
author = {Gabriel, J.-P.},
title = {Martingales with a Countable Filtering Index Set},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 888-898},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995658}
}
Gabriel, J.-P. Martingales with a Countable Filtering Index Set. Ann. Probab., Tome 5 (1977) no. 6, pp. 888-898. http://gdmltest.u-ga.fr/item/1176995658/