A Gaussian correlation inequality and its applications to the existence of small ball constant

Qi-Man Shao

Stochastic Processes and their Applications, 2003, vol. 107, issue 2, 269-287

Abstract: Let X1,...,Xn be jointly Gaussian random variables with mean zero. It is shown that [for all]x>0 and [for all]1[less-than-or-equals, slant]k 0 such that for any 0 0 and y>0. As an application, it is proved that the small ball constant for the fractional Brownian motion of order [alpha] exists.

Keywords: Gaussian; correlation; conjecture; Small; ball; problem; Fraction; Brownian; motion (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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