Optimality of an explicit series expansion of the fractional Brownian sheet

2005 ◽  
Vol 71 (4) ◽  
pp. 295-301 ◽  
Author(s):  
Kacha Dzhaparidze ◽  
Harry van Zanten
Keyword(s):  
Series Expansion ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet

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

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Charles El-Nouty
Keyword(s):  
General Result ◽  
Gaussian Processes ◽  
Brownian Sheet ◽  
Random Vectors ◽  
Fractional Brownian Sheet ◽  
Integral Test ◽  
Small Ball Probability ◽  
Small Ball ◽  
Sufficiency Part ◽  
Necessity Part

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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