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.

Performance evaluation of transport layer protocols in cognitive radio sensor networks (CRSNs) is useful to provide quality-of-service for real-time reliable applications. This paper develops an analytical framework to model the steady-state sending rate of collecting cognitive radio (CR) sensors in rate-based generic additive-increase multiplicative-decrease (AIMD) and additive-increase additi...

In the existing “direct” white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an It6 stochastic differential equation, while a “finitely additive” white noise is used to model the observation noise. We remove this asymmetry by modelling the state process as the solution of a (stochastic) differential equation with a “finitely additive” wh...

When there are covariate effects to be considered, multistate survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox’s (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox’s model in a general finite-state Markov process set...