We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include areaand perimeter-interacting point processes (with stochastic grains), invariant measures of loss networks, and the Ising contour and random cluster models. The algorithm does not invo...

We study the ergodic theory of a multitype contact process with equal death rates and unequal birth rates on the d-dimensional integer lattice and regular trees. We prove that for birth rates in a certain interval there is coexistence on the tree, which by a result of Neuhauser is not possible on the lattice. We also prove a complete convergence result when the larger birth rate falls outside o...

Hematopoietic stem cells (HSCs) are characterized by their ability to self-renew and differentiate into all blood lineage cells. The fate decisions of HSCs (self-renewal versus differentiation) are made through the process of cell division and are often compared to "birth" and "death". Stem cells give rise to undifferentiated stem cells (birth) or differentiate into progenitor cells (death). Th...

We consider an infinite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, that is, the proportion of alleles having a given number of copies at a specified time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP w...

Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such e...

Abstract. In this paper we consider some four-parametric, so-called Generalized Pareto-like Frequency Distribution, which have been constructed using stochastic Birth-Death Process in order to model phenomena arising in Bioinformatics (Astola and Danielian, 2007). As examples, two ”real data” sets on the number of proteins and number of residues for analyzing such distribution are given. The co...

A competition process is a continuous time Markov chain that can be interpreted as system of interacting birth-and-death processes, the components which evolve subject to competitive interaction. This paper devoted study long-term behaviour such process, where component increases with linear birth rate and decreases given by function other components. zero an absorbing state for each component,...

Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions.We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-co...

We demonstrate the existence and uniqueness of optimal observation schedules for discrete observation of the simple death process. Optimality is framed in the sense of observing the process at times that maximise the Fisher information for the death rate. We examine the relationship of our designs with those obtained by other authors for the simple birth process. A number of interesting propert...

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...