Electronic Communications in Probability

Donsker-type theorems for correlated geometric fractional Brownian motions and related processes

Peter Parczewski

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We prove a Donsker-type theorem for vector processes of functionals of correlated Wiener integrals. This includes the case of correlated geometric fractional Brownian motions of arbitrary Hurst parameters in $(0,1)$ driven by the same Brownian motion. Starting from a Donsker-type approximation of Wiener integrals of Volterra type by disturbed binary random walks, the continuous and discrete Wiener chaos representation in terms of Wick calculus is effective. The main result is the compatibility of these continuous and discrete stochastic calculi via these multivariate limit theorems.

Article information

Electron. Commun. Probab., Volume 22 (2017), paper no. 55, 13 pp.

Received: 13 February 2017
Accepted: 28 September 2017
First available in Project Euclid: 13 October 2017

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Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60F17: Functional limit theorems; invariance principles 60G22: Fractional processes, including fractional Brownian motion

functional limit theorem fractional Brownian motion Wiener chaos Wick product discrete stochastic calculus

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Parczewski, Peter. Donsker-type theorems for correlated geometric fractional Brownian motions and related processes. Electron. Commun. Probab. 22 (2017), paper no. 55, 13 pp. doi:10.1214/17-ECP91. https://projecteuclid.org/euclid.ecp/1507860212

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