Limiting distribution of the continuity modulus for Gaussian processes with stationary increments

Zakhar Kabluchko

Statistics & Probability Letters, 2009, vol. 79, issue 7, 953-956

Abstract: Let be a Gaussian process with stationary increments, zero mean and a.s.continuous paths, whose variogram [gamma](t) behaves like ct[alpha], c>0, [alpha][set membership, variant](0,2), as t-->0. We show that the continuity modulus of X has asymptotically Gumbel distribution. In the case [alpha]=2, a non-Gumbel limiting distribution is obtained.

Date: 2009
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