On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking I

DOI10.1214/20-EJP534zbMath1469.60040arXiv2006.00590MaRDI QIDQ2024507

Dariusz Buraczewski, Aleksander M. Iksanov, Bohdan Dovgay

Publication date: 4 May 2021

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.00590

zbMATH Keywords

weak convergencerandom environmentGEM distributionBernoulli sieveweighted branching processinfinite occupancy

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Combinatorial probability (60C05) Processes in random environments (60K37) Exchangeability for stochastic processes (60G09)

Related Items (7)

Renewal theory for iterated perturbed random walks on a general branching process tree: Early generations ⋮ On intermediate levels of a nested occupancy scheme in a random environment generated by stick-breaking II ⋮ Renewal theory for iterated perturbed random walks on a general branching process tree: intermediate generations ⋮ Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree ⋮ A functional limit theorem for nested Karlin's occupancy scheme generated by discrete Weibull-like distributions ⋮ Limit theorems for discounted convergent perpetuities ⋮ Late levels of nested occupancy scheme in random environment

Cites Work

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• Regenerative compositions in the case of slow variation: a renewal theory approach
• Functional limit theorems for the number of occupied boxes in the Bernoulli sieve
• On nested infinite occupancy scheme in random environment
• Asymptotic regimes for the occupancy scheme of multiplicative cascades
• Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
• Small counts in the infinite occupancy scheme
• The Bernoulli sieve
• Ordered and size-biased frequencies in GEM and Gibbs' models for species sampling
• A law of the iterated logarithm for the number of occupied boxes in the Bernoulli sieve
• Regenerative random permutations of integers
• Asymptotic laws for compositions derived from transformed subordinators
• Asymptotic laws for regenerative compositions: gamma subordinators and the like
• Regenerative compositions in the case of slow variation
• Extremes and gaps in sampling from a GEM random discrete distribution
• Renewal Theory for Perturbed Random Walks and Similar Processes
• The Bernoulli sieve: an overview
• A phase transition for the heights of a fragmentation tree
• Asymptotics of the occupancy scheme in a random environment and its applications to tries
• Renewal sequences and record chains related to multiple zeta sums
• Weak convergence of random processes with immigration at random times
• A functional limit theorem for general shot noise processes
• Occupancy schemes associated to Yule processes

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