A non-regenerative model of a redundant repairable system: Bounds for the unavailability and asymptotical insensitivity to the lifetime distribution.
A note on a paper by Govil and Kumar
A note on calculating steady state results for an queuing system when the ratio of the arrival rate to the service rate is large.
A note on directed polymers in Gaussian environments.
A note on limiting behaviour of disastrous environment exponents.
A note on percolation on : isoperimetric profile via exponential cluster repulsion.
A note on Poisson approximation.
We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall.It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate conditions, such that p = 1/n Σipi → 0, np → ∞, np2 → 0, then the total variation distance between X1+...+Xn...
A note on quenched moderate deviations for Sinai’s random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is .
A note on quenched moderate deviations for Sinai's random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than ta (0<a<1) from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.
A note on random walk in random scenery
A note on spider walks
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
A note on spider walks
Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.
A note on Talagrand's positivity principle.
A note on the ballistic limit of random motion in a random potential.
A note on the convexity of the expected queue length of the queue with respect to the arrival rate: A third proof.
A note on the diffusive scaling limit for a class of linear systems.
A note on the optimal replacement policy
A system with a single activated unit, which can be in a finite number of states, is considered. Inspections of the system are carried out at discrete time instants. It is possible to replace it by a new one at these moments. The user of the system, by setting down conditions of replacements, wants to maximize his gain, which does not include the rest value of units. On a numerical example it is shown that the frequency of replacements of the unit need not be the greater the longer is the period...
A note on the Poisson disorder problem
A note on the two-sided regulated random walk
A paradox in a queueing network with state-dependent routing and loss.