Imperial College London
Alternate

DrMikkoPakkanen

Faculty of Natural Sciences, Department of Mathematics

Reader in Data Science and Quantitative Finance
 
 
 
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Contact

 

+44 (0)20 7594 8541m.pakkanen Website

 
 
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Location

 

809Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Pakkanen:2016:10.3150/15-BEJ707,
author = {Pakkanen, MS and Réveillac, A},
doi = {10.3150/15-BEJ707},
journal = {Bernoulli},
pages = {1671--1708},
title = {Functional limit theorems for generalized variations of the fractional Brownian sheet},
url = {http://dx.doi.org/10.3150/15-BEJ707},
volume = {22},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We prove functional central and non-central limit theorems for generalizedvariations of the anisotropic d-parameter fractional Brownian sheet (fBs) forany natural number d. Whether the central or the non-central limit theoremapplies depends on the Hermite rank of the variation functional and on thesmallest component of the Hurst parameter vector of the fBs. The limitingprocess in the former result is another fBs, independent of the original fBs,whereas the limit given by the latter result is an Hermite sheet, which isdriven by the same white noise as the original fBs. As an application, wederive functional limit theorems for power variations of the fBs and discusswhat is a proper way to interpolate them to ensure functional convergence.
AU  - Pakkanen,MS
AU  - Réveillac,A
DO  - 10.3150/15-BEJ707
EP  - 1708
PY  - 2016///
SN  - 1350-7265
SP  - 1671
TI  - Functional limit theorems for generalized variations of the fractional Brownian sheet
T2  - Bernoulli
UR  - http://dx.doi.org/10.3150/15-BEJ707
UR  - http://hdl.handle.net/10044/1/25703
VL  - 22
ER  -
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