International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 825-827

A note on dilations and martingales

Martin L. Jones

Mathematics Department, University of Charleston, 66 George Street, Charleston 29424, South Carolina, USA

Received 20 August 1992

Copyright © 1993 Martin L. Jones. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this note is to investigate the effect of dilations on martingales and to give conditions under which a dilated martingale will retain the martingale property. The technique of dilating the joint distribution of a sequence of random variables has applications in optimal stopping theory and the study of “prophet inequalities” where martingales play a significant role.