In this paper we study the delay characteristics of Fair Queueing algorithms with a stochastic comparison approach. In integrated services networks, Fair Queueing (FQ) algorithms have received much attention, because they can guarantee an end-to-end session delay bound when the burstiness of the session traac is bounded, and they ensure the fair allocation of the bandwidth. The delay characteri...

Harris family of distributions models lifetime of a series system when the number of components is a positive random variable. In this paper, we reveal several stochastic comparisons in the Harris family with different tilt parameters and different baseline distributions with respect to the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stochastic orderin...

The topic of the talk were the time approximation of quasi linear stochastic partial differential equations of parabolic type. The framework were in the setting of stochastic evolution equations. An error bounds for the implicit Euler scheme was given and the stability of the scheme were considered.

We propose a generic method for obtaining quickly good upper bounds on the minimal value of a multistage stochastic program. The method is based on the simulation of a feasible decision policy, synthesized by a strategy relying on any scenario tree approximation from stochastic programming and on supervised learning techniques from machine learning.

An ensemble of stochastic nonleaky integrate-and-fire neurons with global, delayed, and excitatory coupling and a small refractory period is analyzed. Simulations with adiabatic changes of the coupling strength indicate the presence of a phase transition accompanied by a hysteresis around a critical coupling strength. Below the critical coupling production of spikes in the ensemble is governed ...

We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone r...

We derive Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which apply to SDE solutions and to multiple stochastic integrals.

We consider the problem of multi-class classification and a stochastic optimization approach to it. We derive risk bounds for stochastic mirror descent algorithm and provide examples of set geometries that make the use of the algorithm efficient in terms of error in k.

LIGO has completed a series of observations searching for evidence of a stochastic gravitational wave background. There has been no detection to date. However the sensitivity of the observations is approaching the Big Bang nucleosynthesis bound. Future observations will provide information that bounds a number of early Universe models of stochastic gravitational waves.

Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join networks are derived using the (max,+)-algebra approach.