Limit theorems for discrete multitype branching processes counted with a characteristic

Kolesko, Konrad; Sava-Huss, Ecaterina

doi:10.1016/j.spa.2023.04.009

Stochastic Processes and their Applications

2023

DOI: 10.1016/j.spa.2023.04.009

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Limit theorems for discrete multitype branching processes counted with a characteristic

Konrad Kolesko

Ecaterina Sava-Huss

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2024

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Gaussian fluctuations for the two-urn model

Kolesko,

Sava-Huss

2024

Adv. Appl. Probab.

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We introduce a modification of the generalized Pólya urn model containing two urns, and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$ added to the urns after n draws, where $J\in\mathbb{N}$ . We provide sufficient conditions under which the random variables $(B_j(n))_{n\in\mathbb{N}}$ , properly normalized and centered, converge weakly to a limiting random variable. The result reveals a similar trichotomy as in the classical case with one urn, one of the main differences being that in the scaling we encounter 1-periodic continuous functions. Another difference in our results compared to the classical urn models is that the phase transition of the second-order behavior occurs at $\sqrt{\rho}$ and not at $\rho/2$ , where $\rho$ is the dominant eigenvalue of the mean replacement matrix.

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Gaussian fluctuations for the two-urn model

Kolesko,

Sava-Huss

2024

Adv. Appl. Probab.

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Limit theorems for discrete multitype branching processes counted with a characteristic

Cited by 1 publication

References 14 publications

Gaussian fluctuations for the two-urn model

Gaussian fluctuations for the two-urn model

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