Abstract
A notion of the positive spatial association is introduced in this paper to analyze spatial dependence of Boolean models with the focus on estimating the long-range spatial dependence. The explicit tail estimates for probabilities of simultaneous damage to two distant spatial regions are obtained using the regular variation method, and the long-range spatial covariance for the Boolean models with heavy-tailed grains is shown to decay at the power-law rate that is smaller than the tail decay rate of grains. Examples and applications to spatial reliability modeling are also discussed.
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The authors would like to sincerely thank the two reviewers for their comments, which led to an improvement of the presentation of this paper.
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First author is supported by NSF grants CMMI 0825960 and DMS 1007556. Second author is supported by NSF grants CMMI 0825928 and CMMI 1000183. Third author is supported by NSF grant CMMI 0825908.
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Li, H., Xu, S.H. & Kuo, W. Asymptotic analysis of simultaneous damages in spatial Boolean models. Ann Oper Res 212, 139–154 (2014). https://doi.org/10.1007/s10479-013-1363-y
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DOI: https://doi.org/10.1007/s10479-013-1363-y