For a sequence of stochastic vectors forming either a forward or a reverse martingale, a Hajek-Renyi type inequality is derived, and its applications in some problems of simultaneous confidence regions are stressed.
Pranab Kumar Sen. "A Hajek-Renyi Type Inequality for Stochastic Vectors with Applications to Simultaneous Confidence Regions." Ann. Math. Statist. 42 (3) 1132 - 1134, June, 1971. https://doi.org/10.1214/aoms/1177693347