Strong Exponential Integrability of Martingales with Increments Bounded by a Sequence of Numbers
A strong exponential bound for the probability tail of a martingale whose increments are uniformly bounded by a sequence of numbers is established. The exponent, which grows to infinity faster than a quadratic polynomial, is a Young function determined by that sequence. The related Orlicz norm of a martingale is estimated, some examples are discussed, and the optimality of the exponent is proven.
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