Generalization of an inequality of Birnbaum and Marshall, with applications to growth rates for submartingales
type: Item
instance of: scholarly article
title: Generalization of an inequality of Birnbaum and Marshall, with applications to growth rates for submartingales
zbMATH Open document ID: 0617.60043
DOI: 10.1016/0304-4149(87)90027-5
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 4001110
zbMATH Keywords: Lenglart's inequality
zbMATH Keywords: submartingale
zbMATH Keywords: Growth of solutions of stochastic differential equations
zbMATH Keywords: strong asymptotic lower bounds
zbMATH Keywords: occupation times
author: Eric V. Slud
reviewed by: R. Mikulevicius
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90027-5
OpenAlex ID: W1983433405
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description: scientific article; zbMATH DE number 4001110