Related papers: Simulating an infinite mean waiting time
In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent…
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…
We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q]=1, and where the birth rate if the population is currently in state…
We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting…
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…
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…
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…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
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…
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…
A method to direct evaluation of expectations for Langevin systems (stochastic differential equations) is proposed. The method is based on a birth-death process which is derived using combinations of dummy variables and It{\^o} formula. As…
Continuous Time Random Maxima (CTRM) are a generalization of classical extreme value theory: Instead of observing random events at regular intervals in time, the waiting times between the events are also random variables with arbitrary…
The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until…
Abstract simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under…
Return-to-baseline is an important method to impute missing values or unobserved potential outcomes when certain hypothetical strategies are used to handle intercurrent events in clinical trials. Current return-to-baseline approaches seen…
We study two time-changed variants of the birth-death process with catastrophe where the time-changing components are the first hitting times of the stable subordinator and the tempered stable subordinator. For both the processes, we derive…
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…
We conduct a review to assess how the simulation of repeated or recurrent events are planned. For such multivariate time-to-events, it is well established that the underlying mechanism is likely to be complex and to involve in particular…
Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient…