General linear-fractional branching processes with discrete time

@article{Lindo2015GeneralLB,
  title={General linear-fractional branching processes with discrete time},
  author={Alexey Lindo and Serik Sagitov},
  journal={Stochastics},
  year={2015},
  volume={90},
  pages={364 - 378}
}
Abstract We study a linear-fractional Bienaymé–Galton–Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads to the linear-fractional distribution formula for an arbitrary observation time, which allows us to establish transparent limit theorems for the subcritical, critical and supercritical cases. Our results extend recent findings for the linear-fractional… 

Regenerative multi-type Galton-Watson processes

The general Perron-Frobenius theorem describes the growth of powers of irreducible non-negative kernels. In the special case of kernels with an atom this result can be obtained using a regeneration

A pathwise iterative approach to the extinction of branching processes with countably many types

We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but

A pathwise approach to the extinction of branching processes with countably many types

Extinction in branching processes with countably many types

Multitype branching processes describe the evolution of populations in which individuals give birth independently according to a probability distribution that depends on their type. In this thesis,

Perron-Frobenius theory for kernels and Crump-Mode-Jagers processes with macro-individuals

TLDR
A new probabilistic interpretation of the general regeneration method in terms of multi-type Galton-Watson processes producing clusters of particles is given, treating clusters as macro-individuals and arriving at a single-type Crump-Mode-Jagers process with a naturally embedded renewal structure.

References

SHOWING 1-10 OF 23 REFERENCES

Linear-fractional branching processes with countably many types

General branching processes in discrete time as random trees

The simple Galton-Watson process describes populations where individuals live one season and are then replaced by a random number of children. It can also be viewed as a way of generating random

The asymptotic composition of supercritical, multi-type branching populations

The life, past and future are described of a typical individual in an old, non-extinct branching population, where individuals may give birth as a point process and have types in an abstract type

Some limit theorems for positive recurrent branching Markov chains: I

In this paper we consider a Galton-Watson process whose particles move according to a Markov chain with discrete state space. The Markov chain is assumed to be positive recurrent. We prove a law of

Markov Chains and Stochastic Stability

TLDR
This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

General branching processes as Markov fields

On the Markov renewal theorem

A Note on the Theory of Moment Generating Functions

in which the integral is assumed to converge for a in some neighborhood of the origin, is called the moment generating function of X. In dealing with certain distribution problems, this function has

Branching Processes

Never doubt with our offer, because we will always give what you need. As like this updated book, you may not find in the other place. But here, it's very easy. Just click and download, you can own