On discrete homogeneous chains

Continuous-time homogeneous Markov chains

Adaptive Importance Sampling on Discrete Markov Chains

In modeling particle transport through a medium, the path of a particle behaves as a transient Markov Chain. We are interested in characteristics of the particle's movement conditional on its starting state which take the form of a \score" accumulated with each transition. Importance sampling is an essential variance reduction technique in this setting, and we provide an adaptive (iteratively u...

Discrete Quantum Markov Chains

A framework for finite-dimensional quantum Markov chains on Hilbert spaces is introduced. Quantum Markov chains generalize both classical Markov chains with possibly hidden states and existing models of quantum walks on finite graphs. Quantum Markov chains are based on Markov operations that may be applied to quantum systems and include quantum measurements, for example. It is proved that quant...

Discrete Time Homogeneous and non-Homogeneous semi-Markov Reliability Models.∗

In this paper, we extend to our knowledge, for the first case, some reliability results obtained using homogeneous semi-Markov processes to the case of non-homogenous semi-Markov modelisation. Moreover, we apply some of our preceding results to give the numerical solutions and so the possibility to treat real life problems for which non-homogeneity in time is important.

Empirical Localization of Homogeneous Divergences on Discrete Sample Spaces

In this paper, we propose a novel parameter estimator for probabilistic models on discrete space. The proposed estimator is derived from minimization of homogeneous divergence and can be constructed without calculation of the normalization constant, which is frequently infeasible for models in the discrete space. We investigate statistical properties of the proposed estimator such as consistenc...