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


Parczewski, Peter



DOI: https://doi.org/10.1214/17-ECP91
URL: https://projecteuclid.org/euclid.ecp/1507860212
Additional URL: https://projecteuclid.org/download/pdfview_1/eucli...
Document Type: Article
Year of publication: 2017
The title of a journal, publication series: Electronic Communications in Probability : ECP
Volume: 22
Issue number: Paper 55
Page range: 1-13
Place of publication: Seattle, WA
Publishing house: University of Washington, Mathematics Department
ISSN: 1083-589X
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II (Neuenkirch 2013-)
Subject: 510 Mathematics
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.

Dieser Eintrag ist Teil der Universitätsbibliographie.




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Parczewski, Peter (2017) Donsker-type theorems for correlated geometric fractional Brownian motions and related processes. Electronic Communications in Probability : ECP Seattle, WA 22 Paper 55 1-13 [Article]


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