A note on dilations and martingales
Martin L. Jones · International Journal of Mathematics and Mathematical Sciences · 1993
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.