Martingale marginals do not always determine convergence
Probability
2015-03-27 v1
Abstract
Baez-Duarte (1971) and Gilat (1972) gave examples of martingales that converge in probability (and hence in distribution) but not almost surely. Here such a martingale is constructed with uniformly bounded increments, and a construction is provided of two martingales with the same marginals, one of which converges almost surely, while the other does not converge in probability.
Keywords
Cite
@article{arxiv.1503.07833,
title = {Martingale marginals do not always determine convergence},
author = {Jim Pitman},
journal= {arXiv preprint arXiv:1503.07833},
year = {2015}
}