Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales
type: Item
instance of: scholarly article
title: Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales
zbMATH Open document ID: 0962.60045
DOI: 10.1016/S0304-4149(98)00069-6
author: Manfred Denker
author: Alok Goswami
author: Rabi Bhattacharya
published in: Stochastic Processes and their Applications
publication date: 2001-01-17T00:00:00Z
review text: Let \(X\) be a scalar Itô diffusion governed by an equation of the form \[ X(t)= x_0 + \int _0^t\{b(X(s))+\beta (X(s)/a)\} ds +\int _0^t \sigma (X(s)) dB(s), \] where \(b\) is thought of as the local drift velocity and \(\beta (x/a)\) the large-scale velocity of \(X\), the spatial scale parameter \(a\) being large. Behaviour of the diffusion exhibits phase changes as time increases through the different time zones. Four different temporal regimes are identified: an initial non-Gaussian phase for times that are not large followed by a first Gaussian phase, which breaks down over a subsequent region of time, and a final Gaussian phase different from the earlier phases. The first Gaussian phase is shown to occur for times \(1\ll t\ll a^{2/3}\). Detailed analysis of the final phase is carried out as well.
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1554292
zbMATH Keywords: periodic coefficients
zbMATH Keywords: Gaussian approximation
MaRDI profile type: Publication
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full work available at URL: s0304-4149(98)00069-6
OpenAlex ID: W2024006965
description: scientific article; zbMATH DE number 1554292