A multiflow approximation to diffusions
type: Item
instance of: scholarly article
title: A multiflow approximation to diffusions
zbMATH Open document ID: 0734.60080
DOI: 10.1016/0304-4149(91)90044-D
author: Yali Amit
published in: Stochastic Processes and their Applications
publication date: 1991-01-01T00:00:00Z
review text: The author introduces a new form of approximation to diffusions represented as solutions of stochastic differential equations. In the various forms of approximations, one solves a sequence of ordinary differential equations which are derived by substituting, in place of Brownian path, a piecewise differentiable approximation corresponding to a given partition. Then for a given fixed partition, one must solve a new set of differential equations for each Brownian path. To overcome this difficulty, author introduces the so-called multiflow approximation. Here, the approximants are generated by products of the flows of the vector fields defining the stochastic differential equation. Under certain smoothness conditions, it is proved that the approximants converge to a diffusion as the mesh-size of the partitions go to zero. For time independent vector fields on a manifold, the approximants are considered as homogeneous Markov chains, and it is shown that the invariant probability measures of a sequence of approximating Markov chains converge weakly to an invariant probability measure of a diffusion.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 4215103
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: Brownian path
zbMATH Keywords: piecewise differentiable approximation
zbMATH Keywords: smoothness conditions
zbMATH Keywords: invariant probability measure of a diffusion
MaRDI profile type: Publication
cites work: Ergodic properties of markov processes driven by a set of vector fields
cites work: Q3838653
cites work: Q4105055
cites work: Q3959169
cites work: Q3217380
cites work: Q5585820
cites work: Q4043889
cites work: Orbits of Families of Vector Fields and Integrability of Distributions
description: scientific article; zbMATH DE number 4215103