Asymptotic arc-sine laws for finite-dimensional interacting diffussion
type: Item
instance of: scholarly article
title: Asymptotic arc-sine laws for finite-dimensional interacting diffussion
zbMATH Open document ID: 1141.60040
author: Tadashi Noda
published in: Osaka Journal of Mathematics
publication date: 2008-02-22T00:00:00Z
review text: Consider finite-dimensional interacting diffusion processes governed by \[ dX_i(t) = \alpha(X_i(t)) dW_i(t) + \sum_{j \in S} A_{ij} (X_j(t)-X_i(t)) dt ,\quad i \in S, t \geq 0, \] where \((W_i)_{i \in S}\) is a system of independent, one-dimensional standard Wiener processes, \((A_{ij})\) a matrix with nonnegative elements, \(S\) a finite set and \(\alpha : \mathbb{R} \to \mathbb{R}_+\) is a Borel-measurbale function of linearly bounded growth. The author proves that the distribution of related occupation time at the first quadrant \(\mathbb{R}_+^S = [0,\infty)^S\) of \(\mathbb{R}^S\) given by \[ \frac{1}{t} \int^t_0 I_{\mathbb{R}_+^S} (X(u)) du \] converges to a generalized arc-sine law as \(t\) tends to \(+\infty\).
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 5238851
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: interacting diffusions
zbMATH Keywords: interacting particle systems
zbMATH Keywords: occupation time at the first quadrant
zbMATH Keywords: generalized arc-sine law
MaRDI profile type: Publication
Recommended article: On a generalized arc-sine law for one-dimensional diffusion processes
Recommended article: Q4839093
Recommended article: Q3350424
Recommended article: Asymptotic behaviour for a diffusion equation governed by nonlocal interactions.
Recommended article: Q3412491
Recommended article: Asymptotics of kink-kink interaction for sine-Gordon type equations
Recommended article: Q4952128
Recommended article: Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions
Recommended article: Infinite-dimensional diffusion processes with singular interaction
Recommended article: Q4396851
description: scientific article