An ergodic theorem related to some limit theorems for additive functionals of complex Brownian motion
type: Item
instance of: scholarly article
title: An ergodic theorem related to some limit theorems for additive functionals of complex Brownian motion
zbMATH Open document ID: 0798.60076
author: Youichi Yamazaki
published in: Journal of Mathematics of Kyoto University
publication date: 1994-11-01T00:00:00Z
review text: The author proves an ergodic theorem for diffusions. We state one application: Let \(z\) be a complex Brownian motion, \(f \in L^ 1 \cap L^ p\) and \(u(t) = e^{2t} -1\). Then \(\lim_{\lambda \to \infty} \lambda^{-1/2} \int^{u(\sqrt \lambda t)}_ 0 f(z(s))ds\) converges in the sense of finite-dimensional distributions. This extends earlier results in this direction. Other applications are also given.
reviewed by: Murali Rao
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 584576
zbMATH Keywords: additive functional
zbMATH Keywords: ergodic theorem
zbMATH Keywords: complex Brownian motion
zbMATH Keywords: finite- dimensional distributions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519123
OpenAlex ID: W1938800989
DOI: 10.1215/KJM/1250519123
description: scientific article; zbMATH DE number 584576