Electronic Journal of Probability

On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property

Antoine Lejay

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We study the limit of functionals of stochastic processes for which an homogenization result holds. All these functionals involve stochastic integrals. Among them, we consider more particularly the Levy area and those giving the solutions of some SDEs. The main question is to know whether or not the limit of the stochastic integrals is equal to the stochastic integral of the limit of each of its terms. In fact, the answer may be negative, especially in presence of a highly oscillating first-order differential term. This provides us some counterexamples to the theory of good sequence of semimartingales.

Article information

Electron. J. Probab., Volume 7 (2002), paper no. 18, 18 pp.

Accepted: 19 September 2002
First available in Project Euclid: 16 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K40: Other physical applications of random processes

stochastic differential equations good sequence of semimartingales conditions UT and UCV Lévy area

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Lejay, Antoine. On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property. Electron. J. Probab. 7 (2002), paper no. 18, 18 pp. doi:10.1214/EJP.v7-117. https://projecteuclid.org/euclid.ejp/1463434891

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