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

2010 Mathematics Subject Classification: 60J80.

Discrete Time Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Time to Extinction in Branching Processes and its Application in Epidemiology

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

On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

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.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

A Note on the Extinction Problem for Controlled Multitype Branching Processes

2000 Mathematics Subject Classification: 60J80, 60J10.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

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

2000 Mathematics Subject Classification: 60J80.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.

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

2000 Mathematics Subject Classification: 60J80, 62M05

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

2010 Mathematics Subject Classification: 60J80.