International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 825-827
doi:10.1155/S016117129300105X

A note on dilations and martingales

Abstract

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.