A0161
Title: A stochastic maximal inequality and its applications
Authors: Yoichi Nishiyama - Waseda University (Japan) [presenting]
Abstract: It is well known that maximal inequalities play a key role in the fields such as weak convergence of random fields and high-dimensional statistics. Some approaches based on Bernstein's inequality for martingales have been successfully taken to obtain maximal inequalities for martingales. A new inequality, which may be called a stochastic maximal inequality, is presented. The inequality is a bound for maxima of a finite number of martingales by the sum of a predictable increasing process and a martingale starting from zero. It may be regarded as an inequality version of the Doob-Meyer decomposition. As its applications, some analogues of Doob's inequality and Lenglart's inequality to finite-dimensional martingales are obtained. Some applications to statistics will also be discussed.
