Asymptotic analysis of simultaneous damages in spatial Boolean models

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.