On the Lower Classes of Some Mixed Fractional Gaussian Processes with Two Logarithmic Factors | Zendy

Charles El-Nouty | Zendy

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On the Lower Classes of Some Mixed Fractional Gaussian Processes with Two Logarithmic Factors

Author(s) -

Charles El-Nouty

Publication year - 2008

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2008/160303

Subject(s) - mathematics , logarithm , statistic , gaussian , fractional brownian motion , test statistic , ball (mathematics) , norm (philosophy) , brownian motion , statistics , mathematical analysis , statistical hypothesis testing , physics , quantum mechanics , political science , law

We introduce the fractional mixed fractional Brownian sheet and investigate the small ball behavior of its sup-norm statistic by establishing a general result on the small ball probability of the sum of two not necessarily independent joint Gaussian random vectors. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test

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