In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical “unbiased behavior” with exponential distribution of the gaps between appearances, is commonly observed in experimental processes and often difficult to explain. In the last section we relate one such empirical example of clustering, in the area of marine technology. In the theoretical part of the paper...

Dans cet article nous démontrons un théorème de stabilité des probabilités de retour sur un groupe localement compact unimodulaire, séparable et compactement engendré. Nous démontrons que le comportement asymptotique de F*(2n)(e) ne dépend pas de la densité F sous des hypothèses naturelles. A titre d’exemple nous établissons que la probabilité de retour sur une large classe de groupes résolubles se comporte comme exp(−n1/3).

As part of global climate change an accelerated hydrologic cycle (including an increase in heavy precipitation) is anticipated (Trenberth [20, 21]). So, it is of great importance to be able to quantify high-impact hydrologic relationships, for example, the impact that an extreme precipitation (or temperature) in a location has on a surrounding region. Building on the Multivariate Extreme Value Theory we propose a contagion index and a stability index. The contagion index makes it possible to quantify...

This paper examines appropriate protocols for high speed multiple access communication systems where the bandwidth is divided into two separate asymmetric channels. Both channels operate using slotted non-persistent CSMA or CSMA/CD techniques. Free stations access the first channel while all retransmissions occur in the second channel. We define the stability regions and the rules for optimal bandwidth allocation among the two channels for improvement of the system performance in case of infinite...

We study the ergodicity of a multi-class queueing model via fluid limits which have the advantage of describing the model in macroscopic form. We consider a model of processing bandwidth requests. Our system is defined by a network of capacity C=N, and a queue which contains an infinite number of items of various sizes 1, a' and b' with 1 < a' < b' < N. The problem considered is: Under what conditions on the parameters of some large classes of networks, do they reach the stationary regime?...

The upper bounds of the uniform distance $\rho \left({\sum }_{k=1}^{\nu }{X}_k,{\sum }_{k=1}^{\nu }{\tilde{X}}_k\right)$ between two sums of a random number $\nu$ of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.

We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space $X$. It is supposed that an unknown transition probability $p(·|x)$, $x\in X$, is approximated by the transition probability $\tilde{p}(·|x)$, $x\in X$, and the stopping rule ${\tilde{\tau }}_{*}$, optimal for $\tilde{p}$, is applied to the process governed by $p$. We found an upper bound for the difference between the total expected cost, resulting when applying ${\tilde{\tau }}_{*}$, and the minimal total expected cost. The bound given is a constant times ${\displaystyle {sup}_{x\in X}\parallel p(·|x)-\tilde{p}(·|x)\parallel }$, where $\parallel ·\parallel$ is the total variation...

Let $\lambda$ denote the failure rate function of the $d,f$. $F$ and let ${\lambda }_1$ denote the failure rate function of the mean residual life distribution. In this paper we characterize the distribution functions $F$ for which ${\lambda }_1=c\lambda$ and we estimate $F$ when it is only known that ${\lambda }_1/\lambda$ or ${\lambda }_1-c\lambda$ is bounded.

The paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical...

Stability of an invariant measure of stochastic differential equation with respect to bounded pertubations of its coefficients is investigated. The results as well as some earlier author's results on Liapunov type stability of the invariant measure are applied to a system describing molecular rotation.