New Optional Stopping Theorems and Maximal Inequalities on Stochastic Processes
Probability
2012-08-01 v2 Statistics Theory
Statistics Theory
Abstract
In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of stochastic processes over the whole range of time indexes.
Cite
@article{arxiv.1207.3733,
title = {New Optional Stopping Theorems and Maximal Inequalities on Stochastic Processes},
author = {Xinjia Chen},
journal= {arXiv preprint arXiv:1207.3733},
year = {2012}
}
Comments
25 pages, no figure. Fixed some typos. The main results of this paper have appeared in Proceedings of SPIE Conferences, Baltimore, Maryland, April 24-27, 2012