相关论文: Stochastic Comparisons between hitting times for M…

We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains -- an approach that (sometimes) deepens understanding of the…

In the present paper, we investigate the relationship between hitting times and hitting probabilities in discrete-time imprecise Markov chains (IMCs). We define lower and upper hitting times and probabilities for IMCs whose set of…

We study the problem of characterizing the expected hitting times for a robust generalization of continuous-time Markov chains. This generalization is based on the theory of imprecise probabilities, and the models with which we work…

We consider the problem of characterising expected hitting times and hitting probabilities for imprecise Markov chains. To this end, we consider three distinct ways in which imprecise Markov chains have been defined in the literature: as…

A well-known theorem for an irreducible skip-free chain with absorbing state $d$, under some conditions, is that the hitting (absorbing) time of state $d$ starting from state 0 is distributed as the sum of $d$ independent geometric (or…

In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent…

In the absence of acceleration, the velocity formula gives "distance travelled equals speed multiplied by time". For a broad class of Markov chains such as circulant Markov chains or random walk on complete graphs, we prove a probabilistic…

In a recent paper, Shah [arXiv:2502.03073] derived an explicit expression for the distribution of occupancy times for a two-state Markov chain, using a method based on enumerating sample paths. We consider here the more general problem of…

An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling…

In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of "strong metastability time" is introduced to…

There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and…

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…

Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space.…

General characterizations of ergodic Markov chains have been developed in considerable detail. In this paper, we study the transience for discrete-time Markov chains on general state spaces, including the geometric transience and algebraic…

Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work…

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…

Consider a discrete time, ergodic Markov chain with finite state space which is started from stationarity. Fill and Lyzinski (2014) showed that, in some cases, the hitting time for a given state may be represented as a sum of a geometric…