Generalization of an inequality of Birnbaum and Marshall, with applications to growth rates for submartingales
Using Lenglart's inequality the inequality of Birnbaum and Marshall is improved and generalised. The author estimates the probability that \(\sup \{X_ sh_ s:\) \(0\leq s<T\}\geq 1\), where X is a submartingale and h is a nonnegative nonincreasing predictable process. The results are applied to give growth rates for a general submartingale in terms of the compensator of its positive part. Growth of solutions of stochastic differential equations and strong asymptotic lower bounds on Brownian motion occupation times are also considered.
Growth of solutions of stochastic differential equations
scientific article; zbMATH DE number 4001110
scientific article