Related papers: On some transformations of bilateral birth-and-dea…

This paper aims to clarify certain aspects of the relations between birth-death processes, measures solving a Stieltjes moment problem, and sets of parameters defining polynomial sequences that are orthogonal with respect to such a measure.…

For birth and death chains, we derive bounds on the spectral gap and mixing time in terms of birth and death rates. Together with the results of Ding et al. in 2010, this provides a criterion for the existence of a cutoff in terms of the…

The fractional birth and the fractional death processes are more desirable in practice than their classical counterparts as they naturally provide greater flexibility in modeling growing and decreasing systems. In this paper, we propose…

We compute the posterior distributions of the initial population and parameter of binary branching processes, in the limit of a large number of generations. We compare this Bayesian procedure with a more na\"ive one, based on hitting times…

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…

Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every…

A novel approach is employed and developed to derive transition probabilities for a simple time-inhomogeneous birth-death process. Algebraic probability theory and Lie algebraic treatments make it easy to treat the time-inhomogeneous cases.…

The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…

We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with…

We consider a hybrid method to simulate the return time to the initial state in a critical-case birth--death process. The expected value of this return time is infinite, but its distribution asymptotically follows a power-law. Hence, the…

We finely describe the "coming down from infinity" for birth and death processes which eventually become extinct. Our biological motivation is to study the decrease of regulated populations which are initially large. Under general…

This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

In this paper we study strong solutions of some non-local difference-differential equations linked to a class of birth-death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of…

This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…

A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…

We consider a stochastic spatial point process with births and deaths on $\mathbb{R}^d$, with the hard-core property that at any time the balls of radius half of any two points do not overlap. We give explicit construction of the process.…

We here discuss the process of opinion formation in an open community where agents are made to interact and consequently update their beliefs. New actors (birth) are assumed to replace individuals that abandon the community (deaths). This…

In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and…

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending…