Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

Estimation of the Offspring and Immigration Mean Vectors for Bisexual Branching Processes with Immigration of Females and Males

2000 Mathematics Subject Classification: 60J80, 62M05.

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classi cation: 60J80.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

Comparison between Numerical and Simulation Methods for Age-dependent Branching Models with Immigration

2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Population

2000 Mathematics Subject Classification: primary 60J80; secondary 60J85, 92C37.

Lp Microlocal Supercritical Markov Branching Processes with Non-Homogeneous Poisson Immigration

2010 Mathematics Subject Classification: 60J80.

Some Probabilistic Results in a Bisexual Branching Process with Immigration

2000 Mathematics Subject Classification: 60J80.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80.

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.

Parametric Estimation in Branching Processes with an Increasing Random Number of Ancestors

2000 Mathematics Subject Classification: 60J80, 62M05

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05