For a probability measure $$ \mu on SL_d({\mathbb {R}}) , we consider the Furstenberg stationary \nu space of flags. Under general non-degeneracy conditions, if is discrete and \sum _g \log \Vert g\Vert \, (g) < + \infty then exact-dimensional.

A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a β-power time change in the classical Fréchet extremal process, for β in a subinterval of the unit interval. Any such power time change in the extremal process for 0 < β < 1 produces a process with stationary max-increments. This deceptively simple time change...

n≥0 where T denotes the shift on Ω. Conditioned on the particle having asymptotic mean velocity equal to any given ξ, we show that the empirical process of the environment Markov chain converges to a stationary process μ ξ under the averaged measure. When d ≥ 3 and ξ is sufficiently close to the typical velocity, we prove that averaged and quenched large deviations are equivalent and when condi...

This paper studies a continuous sampling plan in preventing entries of defective products produced for sales using queueing theory methods. The sampling plan considered here has three inspection modes. All the products are inspected in mode I and in modes II and III the products are inspected with some probability c ? 0 and d > 0 respectively in the modes in order to avoid high cost of inspecti...

This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and Pötscher (2007). More specifically, their bracketing metric entropy bounds are extended to a norm defined in Doukhan, Massart and Rio (1995, henceforth DMR) that depends both on the marginal distribution o...

The present paper gives the background to point processes in space and time. Some special types of spatial and spatio-temporal models of point processes are introduced with the emphasis to Cox processes. Their basic properties are described and some characteristics are calculated. The simulation of one of these models is shown. Introduction At present, the theory of point processes is well esta...

Many mathematical models exist for describing the behavior of TCP/IP under an exogenous loss process that does not depend on the window size. The goal of this paper is to present a mathematical analysis of two asymmetric competing TCP connections where loss probabilities are directly related to their instantaneous window size, and occur when the sum of throughputs attains a given level. We obta...

Self-stabilizing processes are non-markovian diffusions. The own law of the process intervenes in the drift. When the non-interacting part of the drift corresponds to the gradient of a convex potential, it has been proved in some different ways that such processes converge when the time goes to infinity. However, in a previous paper, it has been proved that there is non-uniqueness of the statio...

We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to...

We examine the conditions for the existence of spectrally stable neutral modes in a Vlasov-Poisson plasma and show that for stable equilibria of systems that have unbounded spatial domain, the only possible neutral modes are those with phase velocities that correspond to stationary inflection points of the equilibrium distribution function. It is seen that these neutral modes can possess positi...