Coupling methods for multidimensional diffusion processes
type: Item
instance of: scholarly article
title: Coupling methods for multidimensional diffusion processes
zbMATH Open document ID: 0686.60083
author: Shao-Fu Li
author: Mu-Fa Chen
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: Probability measures \(P^{x,y}\), \(x,y\in R^ d\), on \(C([0,\infty);R^{2d})\) are considered, such that the canonical process \(Z(t)=(X(t),Y(t))\), \(t\geq 0\), is the \(P^{x,y}\)-diffusion process with the matrix of diffusion coefficients \(a(x,y)=\left( \begin{matrix} a(x)\\ c(x,y)^*\end{matrix} \begin{matrix} c(x,y)\\ a(y)\end{matrix} \right)\) and the vector of drift coefficients \(b(x,y)=(b(x)\quad \quad b(y))'\). Criteria are found for the success of coupling, i.e. \[ P^{x,y}\{T<\infty \}=1\quad and\quad P^{x,y}\{X(t)=Y(t),\quad t\geq T\}=1, \] where \(T=\inf \{t\geq 0:\) \(X(t)=Y(t)\}\). Some examples and applications are also studied.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J70
zbMATH DE Number: 4124760
zbMATH Keywords: multidimensional diffusion processes
zbMATH Keywords: coupling
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991501
OpenAlex ID: W2070893852
DOI: 10.1214/AOP/1176991501
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description: scientific article; zbMATH DE number 4124760