Open Access
2013 Wong-Zakai type convergence in infinite dimensions
Arnab Ganguly
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Electron. J. Probab. 18: 1-34 (2013). DOI: 10.1214/EJP.v18-2650


The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finite-dimensional Brownian motion. In particular, a general form of the correction factor is derived. Examples are given illustrating the use of the theorems to obtain other kinds of approximation results.


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Arnab Ganguly. "Wong-Zakai type convergence in infinite dimensions." Electron. J. Probab. 18 1 - 34, 2013.


Accepted: 5 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1287.60071
MathSciNet: MR3035759
Digital Object Identifier: 10.1214/EJP.v18-2650

Primary: 60H05
Secondary: 60F , 60H10 , 60H20

Keywords: Banach space-valued semimartingales , H^#-semimartingales , infinite-dimensional semimartingales , Stochastic differential equation , uniform tightness , weak convergence , Wong-Zakai

Vol.18 • 2013
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