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Consider the following birth and death process with the following infinitesimal transition probabilities {\lambda}(k) ={\lambda}/(1+k) and {\mu}(k) = {\mu}k with {\lambda},{\mu}> 0. This process has known as a discouragement queue [5].…

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even…

Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…

Sufficient conditions are developed for a class of generalized Polya urn schemes ensuring exchangeability. The extended class includes the Blackwell-MacQueen Polya urn and the urn schemes for the two-parameter Poisson-Dirichlet process and…

The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\nu_k}(t)$, $t\ge 0$, are governed by time-fractional equations of order $0<\nu_k\leq 1$ depending on the number $k$ of events…

We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from…

A method yielding simple relationships among bilateral birth-and-death processes is outlined. This allows one to relate birth and death rates of two processes in such a way that their transition probabilities, first-passage-time densities…

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for…

We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS…

We introduce a class of birth-and-death Polya urns, which allow for both sampling and removal of observations governed by an auxiliary inhomogeneous Bernoulli process, and investigate the asymptotic behaviour of the induced allelic…

The paper studies the counting process arising as a subset of births and deaths in a birth--death process on a finite state space. Whenever a birth or death occurs, the process is incremented or not depending on the outcome of an…

This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of…

We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…

A birth-death chain is a discrete-time Markov chain on the integers whose transition probabilities $p_{i,j}$ are non-zero if and only if $|i-j|=1$. We consider birth-death chains whose birth probabilities $p_{i,i+1}$ form a periodic…

We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We…

We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…

We study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha^{th}$ power $(\alpha >1)$ of the existing number of balls. We…

There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of…