Related papers: Multi-state model with temporal-consistent surviva…
Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this…
In confirmatory clinical trials, survival outcomes are frequently studied and interim analyses for efficacy and/or futility are often desirable. Methods such as the log rank test and Cox regression model are commonly used to compare…
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 this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…
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…
The COVID-19 pandemic has been characterised by multiple waves of transmission driven by interventions and emerging variants, challenging epidemic models that assume gradually evolving transmission dynamics. We propose a class of…
We study perturbation theory and uniform ergodicity for discrete-time Markov chains on general state spaces in terms of the uniform moments of the first hitting times on some set. The methods we adopt are different from previous ones. For…
This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in…
Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that…
We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth…
We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain.…
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…
Predicting the near-future delay with accuracy for trains is momentous for railway operations and passengers' traveling experience. This work aims to design prediction models for train delays based on Netherlands Railway data. We first…