A MAXIMAL INEQUALITY FOR STOCHASTIC INTEGRALS
Abstract: Assume that is a cądląg, real-valued martingale starting from zero, is a
predictable process with values in and . This article contains the
proofs of the following inequalities:
(i) If has continuous paths, then
where the constant is the best possible.
(ii) If is arbitrary, then
where is the unique positive number satisfying the equation
. This constant is the best possible.
2010 AMS Mathematics Subject Classification: Primary: 60G42; Secondary:
60G44.
Keywords and phrases: Martingale, sharp inequality.