Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 55, 13 pp.
Donsker-type theorems for correlated geometric fractional Brownian motions and related processes
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.
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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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