Limit theorems for the number of crossings of a fixed plane by certain sequences of generalized diffusion processes
type: Item
instance of: scholarly article
title: Limit theorems for the number of crossings of a fixed plane by certain sequences of generalized diffusion processes
zbMATH Open document ID: 0841.60061
DOI: 10.1007/BF01060407
author: L. V. Goshko
author: M.Ī. Portenko
published in: Ukrainian Mathematical Journal
publication date: 1996-07-18T00:00:00Z
review text: The article is concerned with a weak convergence of generalized diffusion processes to limit ones. The approach is based on using the number of crossings of a fixed plane by a discrete approximation of a process, i.e., by the sequence \(x(0), x(n^{-1}), x(2n^{-1}), \dots,\) where \(n\) is a positive integer. The most part of the article is devoted to the case of \(R^d\)-valued processes \((d > 1)\). Some results for the case \(d = 1\) have been stated as well. It has been established that the relation between the rate of weak convergence to the limit process and the rate of decreasing to zero of the process discretization step substantially affects the limit distribution.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 830572
zbMATH Keywords: weak convergence of generalized diffusion processes
zbMATH Keywords: discrete approximation of a process
reviewed by: N. S. Bratijchuk
MaRDI profile type: Publication
cites work: Q3797999
cites work: Q3197106
cites work: Q4204927
cites work: Q5548525
cites work: Q4001276
cites work: Q3289432
cites work: Q4834148
description: scientific article; zbMATH DE number 830572