Partial divisibility of random sets

Jnaneshwar Baslingker and Biltu Dan

Stochastic Processes and their Applications, 2025, vol. 185, issue C

Abstract: In this article, we ask the following question: Let VX be the void functional of a random closed set X. For which α>0 is VXα a void functional? We answer this question when X is a random subset of a finite set. The result is then generalized to exponents which preserve complete monotonicity of functions on finite lattices. Also, we study the question of approximating an m-divisible random set by infinitely divisible random sets. We prove a theorem analogous to that of Arak’s classical result (Arak, 1981, 1982) on approximating an m-divisible random variable by infinitely divisible random variables.

Keywords: Random sets; Void probabilities; Infinitely divisible random sets; Completely monotone functions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104632

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