Open AccessLimit theorems for a quadratic variation of Gaussian processes
Author(s) -
Raimondas Malukas
Publication year - 2011
Publication title -
nonlinear analysis modelling and control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.734
H-Index - 32
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/na.16.4.14087
Subject(s) - quadratic variation , limit (mathematics) , mathematics , quadratic equation , central limit theorem , sequence (biology) , gaussian , fractional brownian motion , gaussian process , variation (astronomy) , brownian motion , class (philosophy) , statistical physics , pure mathematics , mathematical analysis , statistics , computer science , physics , geometry , quantum mechanics , biology , artificial intelligence , genetics , astrophysics
In the paper a weighted quadratic variation based on a sequence of partitions for a class of Gaussian processes is considered. Conditions on the sequence of partitions and the process are established for the quadratic variation to converge almost surely and for a central limit theorem to be true. Also applications to bifractional and sub-fractional Brownian motion and the estimation of their parameters are provided.
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