This paper deals with the fundamental problem of estimating the distribution function (df) of the duration of the longest path in the stochastic activity network such as PERT network. First a technique is introduced to reduce variance in Conditional Monte Carlo Sampling (CMCS). Second, based on this technique a new procedure is developed for CMCS. Third, a combined approach of simulation and ap...

We study orbital functions associated to finitely generated geometrically infinite Kleinian groups acting on the hyperbolic space $\mathbb{H}^3$, developing a new method based use of Brownian motion. On way, we give some estimates function nilpotent covers compact manifolds, partially answering question asked by M. Pollicott author.

Stochastic model checking requires the computation of steady-state or transient distribution for finite or infinite Markov chains for the evaluation of some formulas implying probabilities. However the numerical analysis of Markov chains is much less efficient than the sophisticated algorithmic techniques such as MTBDD developed for the deterministic model checking. We propose to simplify the n...