Positive martingales and random measures
type: Item
instance of: scholarly article
title: Positive martingales and random measures
zbMATH Open document ID: 0636.60049
author: Jean-Pierre Kahane
published in: Chinese Annals of Mathematics. Series B
publication date: 1987-01-01T00:00:00Z
review text: Let \((Q_ n(t))\), \(n=0,1,...\), be a positive martingale indexed by t (t\(\in T\) compact metric space) and let \(\sigma\) be a measure on T (\(\sigma\in M\) \(+(T))\). \((Q_ n\sigma)\), \(n=0,1,...\), is a sequence of random measures. If \(\int_{T}E Q_ n(t)d\sigma (t)<\infty\) the random measures \(Q_ n\sigma\) converge weakly a.s. to a random measure Q \(\sigma\). Conditions are given to insure either E Q \(\sigma\) \(=0\) or E Q \(\sigma\) \(=\sigma\) (in general E Q \(\sigma\leq \sigma)\). Examples and applications are given (random coverings, Mandelbrot martingales, multiplicative chaos).
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 4036831
zbMATH Keywords: positive martingale
zbMATH Keywords: random measure
zbMATH Keywords: random coverings
zbMATH Keywords: Mandelbrot martingales
zbMATH Keywords: multiplicative chaos
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4036831