Higher-order derivative of local times for space–time anisotropic Gaussian random fields

Zhenlong Chen and Peng Xu

Statistics & Probability Letters, 2024, vol. 214, issue C

Abstract: Let X={X(t),t∈RN} be a centered space–time anisotropic Gaussian random field values in Rd. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of X(t) are studied. Moreover, we show that the derivatives of the local time of X(t) is jointly continuous on Rd×[0,1]N. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.

Keywords: Space–time anisotropic; Derivatives; Local times; Smoothness; Jointly continuous (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110197

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