Our goal in this paper is to show how one could compose some measures of risks, and more precisely Markovian measures of risk, over a Markov chain. We mainly show the convergence of the composition to a limit independent of the starting point, under ergodicity condition of the Markov chain, and risk averse behaviour of the measure.

We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement control measures. show that the large-population dynamics are deterministic and relate to Kermack–McKendrick PDE. Our assumptions minimalistic sense only important requirement is basic reproduction number R0...

The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain equations written reduced density matrices bath ϱB(t) and system ϱS(t). A formal solution in 2nd approximation interaction yields specific extra term related to intrinsic dynamics. This nonlinear matrix ϱS(t), vanishes ...

We state and prove new properties about Doeblin’s ergodicity coefficient for finite Markov chains. We show that this coefficient satisfies a sub-multiplicative type inequality (analogous to the Markov-Dobrushin’s ergodicity coefficient), and provide a novel but elementary proof of Doeblin’s characterization of weak-ergodicity for non-homogeneous chains. Using Doeblin’s coefficient, we illustrat...

In this paper, we describe a link between Markovian binary trees (MBT) and tree-like quasi-birth-anddeath processes (TLQBD) by associating a specific TLQBD to each MBT. The algorithms to compute the matrices Gk in the TLQBD then correspond to the algorithms calculating the extinction probability vector of the MBT. This parallelism leads to a new quadratic algorithm, based on the Newton iteratio...

This paper deals with a recent statistical model based on fuzzy Markov random chains for image segmentation, in the context of stationary and non-stationary data. On one hand, fuzzy scheme takes into account discrete and continuous classes through the modeling of hidden data imprecision and on the other hand, Markovian Bayesian scheme models the uncertainty on the observed data. A non-stationar...

Résumé/Abstract: We consider a risk minimization problem in a continuous-time Markovian regimeswitching financial model modulated by a continuous-time, observable and finitestate Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a proxy of risk. The riskminimization p...

Hierarchical Markovian models are an adequate paradigm for the modeling of complex systems. For the analysis of such models decomposition and aggregation techniques are very important, since the Markov chain described by a complex model often has a size that exceeds the capacity of contemporary computer equipment by orders of a magnitude. A class of hierarchical Markovian models is deened and a...