arXiv Open Access 2022

On functional limit theorems for branching processes with dependent immigration

Sadillo Sharipov
Lihat Sumber

Abstrak

In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that immigration is rowwise $ψ-$mixing and the offspring mean tends to its critical value 1, immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immigration when immigration is $m-$dependent where $m$ may tend to infinity with the row index at a certain rate. In this case the limiting process is a time-changed Wiener process. Our results extend and improve the previous known results in the literature.

Topik & Kata Kunci

Penulis (1)

S

Sadillo Sharipov

Format Sitasi

Sharipov, S. (2022). On functional limit theorems for branching processes with dependent immigration. https://arxiv.org/abs/2204.10654

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2022
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓