A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

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

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

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

2000 Mathematics Subject Classification: 60J80, 62M05

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

Recent Results for Supercritical Controlled Branching Processes with Control Random Functions

2000 Mathematics Subject Classification: 60J80, 60F05

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05

Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

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

2010 Mathematics Subject Classification: 60J80.

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

2010 Mathematics Subject Classification: 60J80.

Time to Extinction in Branching Processes and its Application in Epidemiology

2010 Mathematics Subject Classification: Primary 60J80; Secondary 92D30.

Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

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

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