Hausdorff Measure of the Range of Space–Time Anisotropic Gaussian Random Fields

Wenqing Ni () and Zhenlong Chen ()
Additional contact information
Wenqing Ni: Zhejiang Gongshang University
Zhenlong Chen: Zhejiang Gongshang University

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 264-282

Abstract: Abstract Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ X = { X ( t ) ∈ R d , t ∈ R N } be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed. Under certain mild conditions, we determine the exact Hausdorff measure function for the range $$X([0,1]^N)$$ X ( [ 0 , 1 ] N ) . Our result extends those in Talagrand (Ann Probab 23:767–775, 1995) for fractional Brownian motion and Luan and Xiao (J Fourier Anal Appl 18:118–145, 2012) for time-anisotropic and space-isotropic Gaussian random fields.

Keywords: Space–time anisotropic Gaussian random fields; Strong local nondeterminism; Range; Hausdorff measure; 60G15; 60G17; 60G60 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-019-00964-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00964-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-019-00964-3

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().