English
Related papers

Related papers: Extinction properties of multi-type continuous-sta…

200 papers

We consider a population growth model given by a two-type continuous-state branching process with immigration and competition, introduced by Ma. We study the relative frequency of one of the types in the population when the total mass is…

Probability · Mathematics 2024-06-07 Imanol Nuñez , José Luis Pérez

Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…

Probability · Mathematics 2007-05-23 G. T. Tetzlaff

Motivated by the stochastic Lotka-Volterra model, we introduce discrete-state interacting multitype branching processes. We show that they can be obtained as the sum of a multidimensional random walk with a Lamperti-type change proportional…

Probability · Mathematics 2022-11-28 Maria Clara Fittipaldi , Sandra Palau

We study the speed of extinction of continuous state branching processes in a L\'evy environment, where the associated L\'evy process oscillates. Assuming that the L\'evy process satisfies the Spitzer's condition and the existence of some…

Probability · Mathematics 2021-07-26 Vincent Bansaye , Juan Carlos Pardo , Charline Smadi

We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…

Probability · Mathematics 2009-09-29 Alexander Roitershtein

We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…

Statistics Theory · Mathematics 2020-09-22 Peter Braunsteins , Sophie Hautphenne , Carmen Minuesa

We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…

Probability · Mathematics 2015-08-03 Lucian Beznea , Oana Lupascu

The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton-Watson process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg. Sci.…

Probability · Mathematics 2024-09-10 Miguel González , Pedro Martín-Chávez , Inés del Puerto

We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Markov chains. As the main application we use it to derive a…

Probability · Mathematics 2022-08-31 R. Loeffen , P. Patie , J. Wang

In this paper, for $\alpha\in (1, 2}$ we show that the $\alpha$-stable continuous-state branching process and the associated process conditioned never to become extinct are positive self-similar Markov processes. Understanding the…

Probability · Mathematics 2008-12-08 A. E. Kyprianou , J. C. Pardo

We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made…

Probability · Mathematics 2019-09-06 Lucian Beznea , Iulian Cîmpean , Michael Röckner

The paper has four goals. First, we want to generalize the classical concept of the branching property so that it becomes applicable for historical and genealogical processes (using the coding of genealogies by ($V$-marked) ultrametric…

Probability · Mathematics 2020-05-06 Andreas Greven , Thomas Rippl , Patric Karl Glöde

A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…

Probability · Mathematics 2021-06-22 Lila Greco , Lionel Levine

In this paper, we provide a construction of the so-called backbone decomposition for multitype supercritical superprocesses. While backbone decompositions are fairly well-known for both continuous-state branching processes and…

Probability · Mathematics 2018-03-28 Dorottya Fekete , Sandra Palau , Juan Carlos Pardo , José Luis Pérez

We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…

Probability · Mathematics 2016-12-01 Antonio Murillo-Salas , José Luis Pérez , Arno Siri-Jégousse

We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical…

Probability · Mathematics 2011-03-29 Nicolas Curien , Yuval Peres

Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…

Probability · Mathematics 2007-05-23 Jan M. Swart

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

Probability · Mathematics 2021-12-07 Ágnes Backhausz , Charles Bordenave , Balázs Szegedy

In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \geq 1$ and is…

Probability · Mathematics 2022-03-17 Martin Friesen , Peng Jin , Barbara Rüdiger

he starting process with countable number of types \mu(t) generates a stopped branching process \xi(t). The starting process stops, by falling into the nonempty set S. It is assumed, that the starting process is subcritical, indecomposable…

Statistics Theory · Mathematics 2011-08-09 Iryna Kyrychynska , Ostap Okhrin , Yaroslav Yeleyko