Hitting probabilities of a class of Gaussian random fields

Wenqing Ni and Zhenlong Chen

Statistics & Probability Letters, 2016, vol. 118, issue C, 145-155

Abstract: Let X={X(t),t∈RN} be an (N,d)-Gaussian random field whose components are independent copies of a centered Gaussian random field X0. Under the assumption that the canonical metric E(X0(t)−X0(s))2 is commensurate with γ(∑j=1N∣tj−sj∣Hj), where s=(s1,…,sN),t=(t1,…,tN)∈RN,Hj∈(0,1),j=1,2,…,N and γ(r) is a non-negative function with some mild conditions, upper and lower bounds on the hitting probabilities of X are obtained. To illustrate our results, several examples of Gaussian random fields are given.

Keywords: Hitting probabilities; Gaussian random field; Capacity; Hausdorff measure (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.06.012

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