Related papers: Intertwining of birth-and-death processes
In this paper one presents the extension of the transient analysis of the class of continuous-time birth and death processes defined on non-negative integers with special transitions from and to the origin. From the origin transitions can…
Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. Perron-Frobenius theory ensures the existence of a corresponding positive eigenvector $\varphi$. The goal of the paper is to give bounds on the amplitude…
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by…
Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
The focus of a survival study is partly on the distribution of survival times, and partly on the health or quality of life of patients while they live. Health varies over time, and survival is the most basic aspect of health, so the two…
The physical idea of the natural origin of diseases and deaths has been presented. The fundamental microscopical reason is the destruction of any metastable state by thermal activation of a nucleus of a nonreversable change. On the basis of…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
Splitting trees are those random trees where individuals give birth at constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous…
For a class of time inhomogenous distribution dependent birth-death processes, we derive the well-posedness, $\mathbb{W}_p$-estimate, exponential ergodicity, and uniform in time propagation of chaos. These extend the corresponding results…
In a recent paper in the Journal of Theoretical Probability Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's classical results on first-hitting times of a birth-death process on the nonnegative…
Due to recent advances in synthetic biology and artificial life, the origin of life is currently a hot topic of research. We review the literature and argue that the two traditionally competing "replicator-first" and "metabolism-first"…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
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…
This paper briefly presents an order statistic approach to the time distribution of the first detected event after a primary avalanche breakdown from a mixture of correlated and dark counting processes. The well-known order statistic…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
A natural extension of a right-continuous integer-valued random walk is one which can jump to the right by one or two units. First passage times above a given fixed level then admit a tractable Laplace transform (probability generating…
For any distribution $\pi$ with support equal to $[n] = \{1, 2,..., n \}$, we study the set $\mathcal{A}_{\pi}$ of tridiagonal stochastic matrices $K$ satisfying $\pi(i) K[i,j] = \pi(j) K[j,i]$ for all $i, j \in [n]$. These matrices…
Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not…