Common strict character of some sharp infinite-sequence martingale inequalities

David C. Cox and Robert P. Kertz

Stochastic Processes and their Applications, 1985, vol. 20, issue 1, 169-179

Abstract: A procedure is given for proving strictness of some sharp, infinite-sequence martingale inequalities, which arise from sharp, finite-sequence martingale inequalities attained by degenerating extremal distributions. The procedure is applied to obtain strictness of the sharp inequalities of Cox and Kemperman and of Cox (sharp form of Burkholder's inequality) for all nontrivial martingale difference sequences X0,X1,....

Date: 1985
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