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We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite,strictly...
We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite,strictly...
We consider the estimation of tail probabilities in queues via the nonparametric estimator constructed by simple computing the observed fraction of time that the queue is out in the tail. We show that...
We study the estimation of tail probabilities in a queue via a semi-parametric estimator based on the maximum value of the workload, observed over the sampled time interval. Logarithmic consistency an...
The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has...
In risk management often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for suc...
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
We are interested in estimating probabilities of rare events in the context of com- puter experiments. These rare events depend on the output of a physical model with random input variables. Since t...
We review various inequalities for Mills' ratio (1 - \Phi)/\phi, where \phi and \Phi denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving f...
We provide a representation of reversible-jump Markov chain Monte Carlo as Gibbs sampling with alternating updates of a model indicator and a "palette" of parameters we denote $\bm \psi$. A key innova...
We obtain the rate of growth of long strange segments and the rate of decay of infinite horizon ruin probabilities for a class of infinite moving average processes with exponentially light tails. Th...
There are at least two ways to interpret numerical degrees of belief in terms of betting: 1. You can offer to bet at the odds defined by the degrees of belief. 2. You can make the judgement that a ...
The binomial ideal associated with the intersection axiom of conditional probability is shown to be radical and is expressed as an intersection of toric prime ideals. This solves a problem in algebr...
Probabilities of moderate deviations for randomly indexed sums of independent and identically dmtributed random variables with multidimensional indices are studied. The results presented extend som...
We prove upper estimates for the tail prebabibties: of quadratic and bilinear forms in independent subgaussian randarn vslriabb. These inequalities are used to get upper esthatcs in thc law diterat...

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