Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions

Alexander Iksanov and Valeriya Kotelnikova

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 283-320

Abstract: A nested Karlin’s occupancy scheme is a symbiosis of classical Karlin’s balls-in-boxes scheme and a weighted branching process. To define it, imagine a deterministic weighted branching process in which weights of the first generation individuals are given by the elements of a discrete probability distribution. For each positive integer j, identify the jth generation individuals with the jth generation boxes. The collection of balls is one and the same for all generations, and each ball starts at the root of the weighted branching process tree and moves along the tree according to the following rule: transition from a mother box to a daughter box occurs with probability given by the ratio of the daughter and mother weights.

Keywords: de Haan’s class Π; Functional limit theorem; Infinite occupancy; Nested hierarchy; Random environment; Stationary Gaussian process (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.08.006

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