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Asymptotic behavior of some strongly critical decomposable multi-type Galton-Watson processes with immigration

  • Matyas Barczy
  • Dániel Bezdány
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Abstract

We study the asymptotic behavior of a critical decomposable multi-type Galton-Watson process with immigration whose offspring mean matrix is triangular with diagonal entries 1. Under second-order moment conditions on the offspring and immigration distributions, we establish a functional limit theorem for the sequence of appropriately scaled processes, and describe the limit process as independent squared Bessel processes and some linear combinations of their iterated integral processes. Our work completes and extends some results of Foster and Ney (1978) for some strongly critical decomposable multi-type Galton-Watson processes with immigration.

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Cite

BibTeXRIS
BibTeX
@misc{barczy2026asymptotic,
  title = {{Asymptotic behavior of some strongly critical decomposable multi-type Galton-Watson processes with immigration}},
  author = {Matyas Barczy and Dániel Bezdány},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02069},
  eprint = {2611.02069},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02069},
}
RIS
TY  - UNPB
TI  - Asymptotic behavior of some strongly critical decomposable multi-type Galton-Watson processes with immigration
AU  - Matyas Barczy
AU  - Dániel Bezdány
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02069
UR  - https://arxiv.org/abs/2611.02069
AB  - We study the asymptotic behavior of a critical decomposable multi-type Galton-Watson process with immigration whose offspring mean matrix is triangular with diagonal entries 1. Under second-order moment conditions on the offspring and immigration distributions, we establish a functional limit theorem for the sequence of appropriately scaled processes, and describe the limit process as independent squared Bessel processes and some linear combinations of their iterated integral processes. Our work completes and extends some results of Foster and Ney (1978) for some strongly critical decomposable multi-type Galton-Watson processes with immigration.
ER  -