相关论文: Time to Extinction in Subcritical Two-Sex Branchin…

We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction…

It is well known that a simple, supercritical Bienaym\'e-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where…

This note gives an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex…

It is well-known that conditioning a supercritical (multi-type) branching process on the event that it eventually becomes extinct yields a subcritical branching process. We study the corresponding inverse problem: given a subcritical…

Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…

In this paper we study a 2-type linear-fractional branching process in varying environment with asymptotically constant mean matrices. Let $\nu$ be the extinction time and for $k\ge1$ let $M_k$ be the mean matrix of offspring distribution…

The asymptotic behavior, as $n\rightarrow \infty $ of the conditional distribution of the number of particles in a decomposable critical branching process $\mathbf{Z}% (m)=(Z_{1}(m),...,Z_{N}(m)),$ with $N$ types of particles at moment…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We…

We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…

We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…

We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…

Given that extinction in a bisexual population is certain, we study a way to approximate the time when this extinction occurs. Our study is based on standard tools from Extreme Value Theory, which in practice are very easy to implement. We…

Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let $\nu$ be the extinction time. Under certain conditions, we show that both $P(\nu=n)$ and $P(\nu>n)$ are…

This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping $A$ and a positively…

The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…

In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a…

This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…

In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…