The asymptotic robustness of estimators as a function of a rarity parameter, in the context of
rare-event simulation, is often qualified by properties such as bounded relative error (BRE) …

This article presents several state-of-the-art Monte Carlo methods for simulating and
estimating rare events. A rare event occurs with a very small probability, but its occurrence is …

We consider a linear stochastic fluid network under Markov modulation, with a focus on the
probability that the joint storage level attains a value in a rare set at a given point in time. The …

We develop importance sampling based efficient simulation techniques for three commonly
encountered rare event probabilities associated with random walks having iid regularly …

Estimating rare event probability with accuracy is of great interest for safety and reliability
applications. In this paper, we focus on rare events which can be modeled by a threshold …

In this article, we consider a Gaussian random field f (t) living on a compact set T⊂ R d and
the computation of the tail probabilities P (∫ T ef (t) dt> eb) as b→∞. We design …

We develop our algorithms in the frame of the kinetic VTF model suggested in [5]. A
distinctive feature of this model consists in introducing of the acceleration variable into the …

Let X be the constrained random walk on ℤ+ 2 having increments (1, 0),(-1, 1), and (0,-1)
with respective probabilities λ, µ1, and µ2 representing the lengths of two tandem queues …

An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave U(x,t) under
a stochastic time-dependent force is developed. The dynamics of the soliton wave U(x,t) is …

Efficient simulation of rare events involving sums of heavy-tailed random variables has been
an active research area in applied probability over the last fifteen years. These rare events …