Abstract. We extend the population continuous time Markov chain formalism so that the state space is augmented with continuous variables accumulated over time as functions of component populations. System feedback can be expressed using accumulations that in turn can influence the Markov chain behaviour via functional transition rates. We show how to obtain mean-field differential equations cap...

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we study “multi-person simple random walks” on a graph G with n vertices. There are n persons distributed randomly at the vertices of G. In each step of this di...

This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, reversible chain, it proved that of holds if only spectral gap generator positive. Moreover, equal to gap. For irreversible case, positivity remains a sufficient condition f-ergodicity. The effectiveness these results are illustrated by some typical examples.

51 Abstract— in order to achieve efficient supply chain integration for the processes or activities; the organizations should recognize and understand all the integration challenges of supply chain. Our goal in this paper is to answer the following question, what are the supply chain integration challenges? The reason behind introducing those challenges is the absence of a single source in the ...

We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix Q. We shall present conditions which ensure that any finite μ-invariant probability measure for Q is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes. QUASISTATIONA...

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.

context-dependent modeling is a well-known approach to increase modeling accuracy in continuous speech recognition. the most common way to implement this approach is via triphone modeling. nevertheless, the large number of such models results in several problems in model training, whilst the robust training of such models is often hardly obtained. one approach to solve this problem is via param...

Considering difference equations in discrete space instead of differential equations in Euclidean space, we investigate a probabilistic formula for the solution of the Dirichlet problem for biharmonic functions. This formula involves the expectation of a weighted sum of the pay-offs at the successive times at which the Markov chain is in the complement of the domain. To make the infinite sum co...

due to the effective role of markov models in customer relationship management (crm), there is a lack of comprehensive literature review which contains all related literatures. in this paper the focus is on academic databases to find all the articles that had been published in 2011 and earlier. one hundred articles were identified and reviewed to find direct relevance for applying markov models...

To estimate the premium an investor should expect from extended hedge fund lockups, Derman et al. (2009) proposed a three-state discrete-time Markov Chain to model the state of a hedge fund, allowing the state to change randomly among the states “good,” “sick” and “dead” every year. The lockup premium measures the consequence of being stuck with a sick fund. To be more realistic, we propose an ...