This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of individual nodes in a scale-free network follows some non-homogeneous Markov chains. Exploring the special structure of these Markov chains, we are able to develop an...

This paper establishes a relation between growth networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of individual nodes in a growth network follows non-homogeneous Markov chains. Exploring the special structure of these Markov chains, we are able to develop an efficient al...

Probabilistic model checkers like PRISM check the satisfiability of probabilistic CTL (pCTL) formulas against discrete-time Markov chains. We prove soundness and completeness of their underlying algorithm in Isabelle/HOL. We define Markov chains given by a transition matrix and formalize the corresponding probability measure on sets of paths. The formalization of pCTL formulas includes unbounde...

This paper compares performance of a hidden Markov model (HMM) and a hybrid HMM/ANN model in seismic events modeling. Observation variables are assumed to follow a Poisson distribution. Parameters of the discrete-time two-state models are estimated on the basis of data on seismic events that were recorded in Poland from 1991 to 1995. Then, on the basis of the estimation results, the most likely...

Despite mounting evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. Based on empirical evidence we propose a parsimonious model that is a mixture of (two) Markov chains, where the mixing is on the speed of movement among credit ratings. We estimate this model using credit ratin...

We analyze the quasi-stationary distributions of the family of Markov chains {Xε n }, ε > 0, obtained from small non-local random perturbations of iterates of a map f : I → I on a compact interval. The class of maps considered is slightly more general than the class of one-dimensional Axiom A maps. Under certain conditions on the dynamics, we show that as ε → 0 the limit quasi-stationary distri...