We consider a semi-Markov additive process A(·), i.e., a Markov additive process for which the sojourn times in the various states have general (rather than exponential) distributions. Letting the Lévy processesXi(·), which describe the evolution ofA(·) while the background process is in state i, be increasing, it is shown how double transforms of the type ∫∞ 0 e −qt E[e−αA(t)]dt can be compute...

We derive novel upper and lower finite-length bounds of the error probability in joint source-channel coding when the source obeys the ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive channel. These bounds achieve the tight bounds in the large and moderate deviation regimes. Index Terms Markov chain, joint source-channel coding, finite-l...

The maximum entropy noise under a lag autocorrelation constraint is known by Burg’s theorem to be the th order Gauss–Markov process satisfying these constraints. The question is, what is the worst additive noise for a communication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all noise processes with covaria...

We consider the stationary distribution of the M/GI/1 type queue when background states are countable. We are interested in its tail behavior. To this end, we derive a Markov renewal equation for characterizing the stationary distribution using a Markov additive process that describes the number of customers in system when the system is not empty. Variants of this Markov renewal equation are al...

1. Spectrally Negative Markov Additive Processes. This paper presents some fluctuation identities for a special, but none the less quite general, class of Markov Additive Processes (MAP). Before entering our discussion on the subject we shall simply begin by defining the class of processes we intend to work with and its properties. Following Asmussen and Kella (2000) we consider a process X(t),...

In this paper, we are concerned with centered Markov Additive Processes {(Xt, Yt)}t∈T where the driving Markov process {Xt}t∈T has a finite state space. Under suitable conditions, we provide a local limit theorem for the density of the absolutely continuous part of the probability distribution of tYt given X0. The rate of convergence and the moment condition are the expected ones with respect t...

We study the first passage process of a spectrally-negative Markov additive process (MAP). The focus is on the background Markov chain at the times of the first passage. This process is a Markov chain itself with a transition rate matrix Λ. Assuming time-reversibility we show that all the eigenvalues of Λ are real with algebraic and geometric multiplicities being the same, which allows us to id...