Weak convergence to the multiple Stratonovich integral.
type: Item
instance of: scholarly article
title: Weak convergence to the multiple Stratonovich integral.
zbMATH Open document ID: 1047.60048
DOI: 10.1016/S0304-4149(00)00045-4
author: Xavier Bardina
author: Maria Jolis
published in: Stochastic Processes and their Applications
publication date: 2004-09-22T00:00:00Z
review text: The weak convergence, as \(\varepsilon \) tends to zero, of the multiple integral process \[ \int _0^t \dots \int _0^tf(t_1,\dots ,t_n)\,d\eta _\varepsilon (t_1)\dots \,d\eta _\varepsilon (t_n),\quad t\in [0,T], \] in the space \(\mathcal C_0([0,T])\) is studied, where \(f\in L^2([0,T]^n)\) and \((\eta _\varepsilon (t))_{\varepsilon >0}\) is a family of stochastic processes with absolutely continuous paths that converge weakly to the Brownian motion. The limit is shown to exist if \(f\) is a multimeasure. It also exists under some conditions on \((\eta _\varepsilon )\) if \(f\) is a continuous function of the form \(f(t_1,\dots ,t_n)=f_1(t_1)\dots f_n(t_n)1_{[t_1<\dots <t_n]}\). The limit process is the multiple Stratonovich integral of the function \(f\).
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 2102353
zbMATH Keywords: multiple Stratonovich integral
zbMATH Keywords: multimeasure
zbMATH Keywords: Donsker approximations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2102353