A rich formalization of measure and probability theory is a prerequisite to analyzing probabilistic program behaviour in interactive theorem provers. When using probability theory it is important to have the necessary tools (definitions and theorems) to construct measure spaces with the desired properties. This thesis presents the formalization of a rich set of constructions. We start with disc...

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...

In this article, the Input-to-state stability theory is used to investigate stochastic Cohen–Grossberg bidirectional associative memory neural network with time-varying delay. addition, Markovian jump parameters are considered in model determine continuous-time, discrete-state Markov chain. By utilizing Lyapunov functional and weak infinitesimal generator algebraic conditions derived for criter...

Based on establishing the mathematical model of system provided parameters, using discrete-time Markov chain and a function set by non-negative integer random variable as Probabilistic methods, discrete time variable, two-queue different gated polling has been fully analyzed, low- higher-order properties cycle period are deduced, average queue pair length waiting delay for message packets calcu...

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This is done by considering as basic uncertainty models the so-called credal sets that these probabilities are known or believed to belong to, and by allowing the probabilities to vary over such sets. This leads to the definition of an imprecise M...

Canonical forms of Markovian distributions and processes provide an efficient way of describing these structures by eliminating the redundancy of general representations. Canonical forms of order 2 stationary Markov arrival processes (MAPs) have already been established for both continuous and discrete time. In this paper we present canonical form of continuous time non-stationary MAPs of order...

Deadlocks constitute a major issue in the design and operation of discrete event systems. In automated manufacturing systems, deadlocks assume even greater importance in view of the automated operation. In this paper, we show that Markov chains with absorbing states provide a natural model of manufacturing systems with deadlocks. With illustrative examples, we show that performance indices such...

We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We study the long time behavior of the population and the ancestral lineage of typical individuals under general assumptions, which we specify for applications ...