in this paper at rst, a history of mathematical models is given.next, some basic information about random variables, stochastic processesand markov chains is introduced. as follows, the entropy for a discrete timemarkov process is mentioned. after that, the entropy for sis stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can exten...

We propose a robust estimation algorithm for tracking the location and dynamic motion of a mobile unit in a cellular network. The underlying mobility model is a dynamic linear system driven by a discrete command process that determines the mobile unit’s acceleration. The command process is modeled as a semi-Markov process over a finite set of acceleration levels. Previous approaches to mobility...

This report introduces a new model for event-driven temporal sequence processing: Generalized Hidden Semi-Markov Models (GHSMMs). GHSMMs are an extension of hidden Markov models to continuous time that builds on turning the stochastic process of hidden state traversals into a semi-Markov process. A large variety of probability distributions can be used to specify transition durations. It is sho...

An exponential approximation for a time of the 1st loss of a call and the behaviour of a ow of lost calls for a Markov retrial state-dependent queueing system with nite capacity, operating in Markov environment and in conditions of "fast" service, is studied. The method of proof is based on the results about asymptotic behaviour of the 1st exit time from a xed subset of a semi-Markov process fo...

Vehicles are important elements of military transport systems. Semi-Markov processes, owing to the generic assumption form, a useful tool for modelling operation process numerous technical objects and The suggested approach is an extension existing stochastic methods employed wide spectrum objects; however, research on light utility vehicles complements subject gap in scientific literature. Thi...