The Annals of Probability

On Building Random Variables of a Given Distribution

Gerard Letac

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Abstract

Given $(X_t)_{t\geqq1}$, independent random variables on some measurable space $(I, \mathscr{B})$ with the same distribution $m$, and a positive function $f$ of $L^1(m)$ with $\|f\|_1 = 1$, this paper studies how to build a stopping time $T$ with respect to the $\sigma$-fields $\mathscr{F}_t$ generated $X_1, X_2, \cdots, X_t$, such that the distribution of $X_T$ in $(I, \mathscr{B})$ is exactly $f dm$.

Article information

Source
Ann. Probab., Volume 3, Number 2 (1975), 298-306.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996400

Digital Object Identifier
doi:10.1214/aop/1176996400

Mathematical Reviews number (MathSciNet)
MR375725

Zentralblatt MATH identifier
0302.60028

JSTOR
links.jstor.org

Subjects
Primary: 62E25
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 28A35: Measures and integrals in product spaces

Keywords
Monte-Carlo methods stopping times

Citation

Letac, Gerard. On Building Random Variables of a Given Distribution. Ann. Probab. 3 (1975), no. 2, 298--306. doi:10.1214/aop/1176996400. https://projecteuclid.org/euclid.aop/1176996400


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