We consider weak lumpability of denumerable discrete or continuous time Markov chains. Firstly, we are concerned with irreducible recurrent positive and R-positive Markov chains evolving in discrete time. We study the properties of the set of all initial distributions of the starting chain leading to an aggregated homogeneous Markov chain with respect to a partition of the state space. In parti...

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...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

In this paper, the ambiguity of nite state irreducible Markov chain trajectories is reminded and is obtained for two state Markov chain. I give an applicable example of this concept in President election

A novel method is presented for estimating the parameters of a parametric diffusion process. The approach based on closed-form Maximum Likelihood estimator an approximating Continuous Time Markov Chain (CTMC) Unlike typical time discretization approaches, such as pseudo-likelihood approximations with Shoji-Ozaki or Kessler's method, CTMC approximation introduces no time-discretization error dur...

Excerpted Section A. MARKOV CHAIN APPROXIMATION Another approach to finite differences is the well developed Markov Chain Approximation (MCA) of Kushner [3, 4]. Recent developments are surveyed and further advanced by Kushner [5], and by Kushner and Dupuis [6], with special attention to methods for jump and reflected diffusions. This method applies a Markov chain approximation to continuous tim...

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 the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust e...