A population has two types of individuals, each occupying an island. One of those, where individuals of type 1 live, offers a variable environment. Type 2 individuals dwell on the other island, in a constant environment. Only one-way migration (1 → 2) is possible. We study the asymptotics of the survival probability in critical and subcritical cases.

This paper checks the correctness of our novel algorithm for secure, reliable and flexible transmission of big data in two-hop wireless networks using cooperative jamming scheme of attacker location unknown through Markovian process. Big data has to transmit in two-hop from source-to-relay and relay-to-destination node by deploying security in physical layer. Based on our novel algorithm, the n...

In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the b...

We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M...

We consider the problem of stochastic averaging of a quantum two-state dynamics driven by non-Markovian, discrete noises of the continuous time random walk type (multistate renewal processes). The emphasis is put on the proper averaging over the stationary noise realizations corresponding, e.g., to a stationary environment. A two-state non-Markovian process with an arbitrary non-exponential dis...

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to system backflow of information (strong non-Markovianity) have been experimentally simulated. In this work, using an all-optical setup we simulate and observe the...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X . Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λn along which we will be able to estimate the conditional probability P (Xλn+1 = x|X0, . . . , Xλn) from data segment (X0, . . . , Xλn) in a pointwise consistent way for a restricted ...

In this paper, we identify the batch Markovian arrival process (BMAP) as analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the batch Markovian arrival process such that the different lengths of IP packets are represented by rewards (i.e., batch sizes of arrivals) of the BMAP. The utilization o...

The present paper contains a specification of the EM algorithm in order to fit an empirical counting process, observed at discrete times, to a Markovian arrival process. The given data are the numbers of observed events in disjoint time intervals. The underlying phase process is not observable. An exact numerical procedure to compute the E and M steps is given.