Homogeneous branching processes with non-homogeneous immigration

I Rahimov - Stochastics and Quality Control, 2022 - degruyter.com
The stationary immigration has a limited effect over the asymptotic behavior of the
underlying branching process. It affects mostly the limiting distribution and the life-period of …

Efficient Estimation of Auto-Regression Parameters and Innovation Distributions for Semiparametric Integer-Valued AR(p) Models

FC Drost, R Van den Akker… - Journal of the Royal …, 2009 - academic.oup.com
Integer-valued auto-regressive (INAR) processes have been introduced to model non-
negative integer-valued phenomena that evolve over time. The distribution of an INAR (p) …

Functional limit theorems for critical processes with immigration

I Rahimov - Advances in Applied Probability, 2007 - cambridge.org
We consider a critical discrete-time branching process with generation dependent
immigration. For the case in which the mean number of immigrating individuals tends to∞ …

The asymptotic structure of nearly unstable non-negative integer-valued AR (1) models

FC Drost, R Van Den Akker, BJM Werker - 2009 - projecteuclid.org
This paper considers non-negative integer-valued autoregressive processes where the
autoregression parameter is close to unity. We consider the asymptotics of this 'near unit …

Testing for the extent of instability in nearly unstable processes

M Badreau, F Proïa - Journal of Time Series Analysis, 2023 - Wiley Online Library
This article deals with unit root issues in time series analysis. It has been known for a long
time that unit root tests may be flawed when a series although stationary has a root close to …

A note on asymptotic behavior of critical Galton–Watson processes with immigration

M Barczy, D Bezdány, G Pap - Involve, a Journal of Mathematics, 2022 - msp.org
In this somewhat didactic note we give a detailed alternative proof of the known result of Wei
and Winnicki (1989) which states that, under second-order moment assumptions on the …

A fluctuation limit theorem for a critical branching process with dependent immigration

H Guo, M Zhang - Statistics & Probability Letters, 2014 - Elsevier
A fluctuation limit theorem for a critical branching process with dependent immigration -
ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …

Deterministic approximation of a sequence of nearly critical branching processes

I Rahimov - Stochastic analysis and applications, 2008 - Taylor & Francis
We consider a sequence of discrete time nearly critical branching processes with time-
dependent immigration. Using a martingale approach, we prove that when the immigration …

Unified inference for an integer-valued AR (1) model

L Chen, X Liu, L Peng, F Zhu - Communications in Statistics-Theory …, 2024 - Taylor & Francis
Conditional least squares estimation is often employed to infer an integer-valued AR (1)
model and its convergence rate and asymptotic variance differ for the stable and nearly …

Occupation time fluctuations of weakly degenerate branching systems

Y Li, Y Xiao - Journal of Theoretical Probability, 2012 - Springer
We establish limit theorems for rescaled occupation time fluctuations of a sequence of
branching particle systems in ℝ d with anisotropic space motion and weakly degenerate …