相关论文: Scaling features of two special Markov chains invo…

In this paper we study a particular class of Piecewise deterministic Markov processes (PDMP's) which are semi-stochastic catastrophe versions of deterministic population growth models. In between successive jumps the process follows a flow…

We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…

We consider a discrete time population model for which each individual alive at time $n$ survives independently of everybody else at time $n+1$ with probability $\beta_n$. The sequence $(\beta_n)$ is i.i.d. and constitutes our random…

We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…

The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…

Random population dynamics with catastrophes (events pertaining to possible elimination of a large portion of the population) has a long history in the mathematical literature. In this paper we study an ergodic model for random population…

In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function…

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…

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…

We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…

The cutoff phenomenon describes a case where a Markov chain exhibits a sharp transition in its convergence to stationarity. In 1996, Diaconis surveyed this phenomenon, and asked how one could recognize its occurrence in families of finite…

Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered…

In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…

We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…

This paper contributes an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices $\N_0^d$, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic…

Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

We introduce a class of continuous-time bivariate phase-type distributions for modeling dependencies from common shocks. The construction uses continuous-time Markov processes that evolve identically until an internal common-shock event,…

We study quantitative recurrence to rare events in Countable Markov Shifts with recurrent potentials, focusing on return-time statistics to natural target sets for every point. In the positive recurrent case, return-time processes…

In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…