An Ideal Metric and the Rate of Convergence to a Self-Similar Process

Open Access

1 April 1987

journal article
Published by Institute of Mathematical Statistics in The Annals of Probability

Vol. 15 (2) , 708-727
https://doi.org/10.1214/aop/1176992167

Abstract

A new metric is introduced which is suitable for estimating the rate of convergence of processes related to stable random variables. It is shown that it has an upper bound depending on the difference pseudomoments, but not on the absolute moments. This new metric is then applied to get some rates of convergence to a self-similar process constructed from a stable process.

Keywords

METHOD OF PROBABILITY METRICS
IDEAL METRIC
DIFFERENCE PSEUDOMOMENT
RATE OF CONVERGENCE
STABLE RANDOM VARIABLE
SELF-SIMILAR PROCESS
FRACTIONAL STABLE PROCESS
FRACTIONAL CALCULUS

This publication has 0 references indexed in Scilit: