Deviation inequalities for continuous martingales
type: Item
instance of: scholarly article
title: Deviation inequalities for continuous martingales
zbMATH Open document ID: 0889.60043
DOI: 10.1016/S0304-4149(96)00100-7
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: A class of continuous martingales \(M_t\) is considered that have a locally deterministic modulus in certain sense. It is shown that if they are appropriately normalized by their quadratic variation, then their probabilistic tails are Gaussian. Besides this main result, other consequences of the basic assumption are examined and energy inequalities and results on the smoothness of the sample functions of \(t\mapsto M_t\) are provided. They are used to obtain estimates for the smoothness of continuous additive functionals of multidimensional Brownian motion viewed as functions of their Revuz measures.
reviewed by: Ivan Saxl
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1134786
zbMATH Keywords: Brownian motion
zbMATH Keywords: continuous martingales
zbMATH Keywords: energy inequalities
zbMATH Keywords: Revuz measure
author: D. Khoshnevisan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1134786