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

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  • Kabluchko, Zakhar

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.

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  • Kabluchko, Zakhar, 2009. "Limiting distribution of the continuity modulus for Gaussian processes with stationary increments," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 953-956, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:953-956
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