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Continuity in the Hurst index of the local times of anisotropic Gaussian random fields

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  • Wu, Dongsheng
  • Xiao, Yimin

Abstract

Let be a family of (N,d)-anisotropic Gaussian random fields with generalized Hurst indices H=(H1,...,HN)[set membership, variant](0,1)N. Under certain general conditions, we prove that the local time of is jointly continuous whenever . Moreover we show that, when H approaches H0, the law of the local times of XH(t) converges weakly [in the space of continuous functions] to that of the local time of XH0. The latter theorem generalizes the result of [M. Jolis, N. Viles, Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion, J. Theoret. Probab. 20 (2007) 133-152] for one-parameter fractional Brownian motions with values in to a wide class of (N,d)-Gaussian random fields. The main argument of this paper relies on the recently developed sectorial local nondeterminism for anisotropic Gaussian random fields.

Suggested Citation

  • Wu, Dongsheng & Xiao, Yimin, 2009. "Continuity in the Hurst index of the local times of anisotropic Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1823-1844, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1823-1844
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    References listed on IDEAS

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    Cited by:

    1. Giordano, Luca M. & Jolis, Maria & Quer-Sardanyons, Lluís, 2020. "SPDEs with linear multiplicative fractional noise: Continuity in law with respect to the Hurst index," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7396-7430.

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