## The Annals of Probability

### The Advantage of Using Non-Measurable Stop Rules

#### Abstract

Comparisons are made between the expected returns using measurable and non-measurable stop rules in discrete-time stopping problems. In the independent case, a natural sufficient condition ("preservation of independence") is found for the expected return of every bounded non-measurable stopping function to be equal to that of a measurable one, and for that of every unbounded non-measurable stopping function to be arbitrarily close to that of a measurable one. For non-negative and for uniformly-bounded independent random variables, universal sharp bounds are found for the advantage of using non-measurable stopping functions over using measurable ones. Partial results for the dependent case are obtained.

#### Article information

Source
Ann. Probab., Volume 11, Number 2 (1983), 442-450.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993609

Digital Object Identifier
doi:10.1214/aop/1176993609

Mathematical Reviews number (MathSciNet)
MR690141

Zentralblatt MATH identifier
0529.60041

JSTOR

#### Citation

Hill, Theodore P.; Pestien, Victor C. The Advantage of Using Non-Measurable Stop Rules. Ann. Probab. 11 (1983), no. 2, 442--450. doi:10.1214/aop/1176993609. https://projecteuclid.org/euclid.aop/1176993609