In this paper, sufficient conditions are given for the existence of limiting distribution of a nonhomogeneous countable Markov chain with time-dependent transition intensity matrix. The method of proof exploits the fact that if the distribution of random process Q = (Qt )t 0 is absolutely continuous with respect to the distribution of ergodic random process Q◦ = (Q◦t )t 0, then Qt law −→ t→∞ wh...

Network intrusion occurs when a criminal gains access to a customer's telephone, computer, bank, or other type of account. Detecting network intrusion is an important problem that has received little attention in the statistics literature. This article proposes a Markov modulated nonhomogeneous Poisson process (MMNHPP) to monitor transactions on a customer's account for deviations from the cust...

This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t) and conservative matrix Q(t) = [qij(t)] of nonhomogeneous transition rates qij(t), and use it to construct the transition ...

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.

We present two stochastic failure models for the reliability evaluation of manufacturing equipment that degrades due to its complex operating environment. The first model examines the case when the environment is a temporally nonhomogeneous continuous-time Markov chain, and the second assumes the environment is a temporally homogeneous semi-Markov process on a finite space. Derived are transfor...