New Optional Stopping Theorems and Maximal Inequalities on Stochastic Processes

2012/07/16 by Xinjia Chen, Chen, Xinjia
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Auction Theory and Applications #FOS: Mathematics #Optimization and Search Problems #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1207.3733

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

openalex publication_date 2012/07/16 · arxiv created 2012/07/31 · arxiv updated 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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