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We study certain properties of the function space of autocorrelation functions of Unit Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the $L^p$ norm of the autocorrelation function of arbitrary finite state space CTMCs is infinite. Several interesting inferences are made for point processes associated with CTMCs/ Discrete Time Markov Chains (DTMCs).
Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models computation
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 processes a
This paper is motivated by demands in stochastic reaction network theory. The $Q$-matrix of a stochastic reaction network can be derived from the reaction graph, an edge-labelled directed graph encoding the jump vectors of an associated continuous ti
This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions of continuous-time Markov chains on a subset of the non-negative integers. A new identity for stationary measures is established. In particular, f
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of th