### On the expected diameter of an L2-bounded martingale

Lester E. Dubins, David Gilat, Isaac Meilijson

Speaker: Isaac Meilijson

ABSTRACT

It is shown that the ratio between the expected diameter of an L2-bounded martingale and the standard deviation of its last term cannot exceed sqrt(3).

A stopped Brownian Motion is exhibited for which the upper bound is attained. These results complement the Dubins & Schwarz respective bounds 1 and sqrt(2) for the ratios between the expected maximum and maximal absolute value of the martingale to the standard deviation of its last term.