## Electronic Communications in Probability

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

Peter Parczewski

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ecp/1507860212

Digital Object Identifier
doi:10.1214/17-ECP91

Mathematical Reviews number (MathSciNet)
MR3718705

Zentralblatt MATH identifier
06797808

#### Citation

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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