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Partial divisibility of random sets

Author

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  • Baslingker, Jnaneshwar
  • Dan, Biltu

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.

Suggested Citation

  • Baslingker, Jnaneshwar & Dan, Biltu, 2025. "Partial divisibility of random sets," Stochastic Processes and their Applications, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:spapps:v:185:y:2025:i:c:s0304414925000730
    DOI: 10.1016/j.spa.2025.104632
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