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2017 Donsker-type theorems for correlated geometric fractional Brownian motions and related processes
Peter Parczewski
Electron. Commun. Probab. 22: 1-13 (2017). DOI: 10.1214/17-ECP91

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.

Citation

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Peter Parczewski. "Donsker-type theorems for correlated geometric fractional Brownian motions and related processes." Electron. Commun. Probab. 22 1 - 13, 2017. https://doi.org/10.1214/17-ECP91

Information

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

zbMATH: 06797808
MathSciNet: MR3718705
Digital Object Identifier: 10.1214/17-ECP91

Subjects:
Primary: 60F17 , 60G22 , 60H05

Keywords: discrete stochastic calculus , fractional Brownian motion , Functional limit theorem , Wick product , Wiener Chaos

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