Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...

We consider a system existing in a random environment. The environment is described by a Markov process called Markov environment process (MEP). The system is subject to a sequence of randomly occurring shocks, and each shock causes a random amount of damage which accumulates additively. The shock arrival and shock magnitude are influenced by changes of the environment. The damage process is as...

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.

With the increasing complexity of multiprocessor and distributed processing systems, the need to develop efficient and accurate modeling methods is evident. Fault tolerance and degradable performance of such systems has given rise to considerable interest in models for the combined evaluation of performance and reliability [l], [2]. Markov or semi-Markov reward models can be used to evaluate th...

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random ...

An Edgeworth expansion of a Studentized statistic for an ergodic regenerative strong Markov process is validated. A specific nonparametric bootstrap method is proposed and proved to be second-order correct in the light of the Edgeworth expansion, which is a variant of the regenerative block bootstrap designed for discrete-time Markov processes. One-dimensional diffusions and semi-Markov process...

The first application of Semi-Markov Process (SMP) in actuarial field was given by J. Janssen [6]. Many authors successively used these processes and their generalizations In some books it is also shown how it is possible to use these processes in actuarial science, (see Pitacco, Olivieri, [10], CMIR12 [12]).These processes can be generalised introducing a reward structure see for example Howar...

Correlated node behavior poses a great challenge for normal functioning of mobile ad hoc network. The impact could be devastating if the spreading of correlated node behavior will result in network failure. We model correlated node behavior by merging the principle of epidemic model and semi Markov process. Under merging condition, node behavior transition and epidemic model is converge to capt...