This discussion paper resulted in a publication in the <I>Siam Journal on Matrix Analysis and Applications (2011). Volume 32, issue 3, pages 665-684.<P> A sequence of real numbers (<I>x_n</I>) is Benford if the significands, i.e. the fractionparts in the floating-point representation of (<I>x_n</I>), are distributed...</i></i></p></i>

This discussion paper resulted in a publication in the <I>Mathematical Methods of Operations Research</I> (2005). Volume 62, issue 3, pages 467-483.<P> We develop a methodology for studying "large deviations type" questions. Our approach does not require that the large deviations principle holds, and is...</p></i>

In: <I>Proceedings Winter Simulation Conference</I>, 9-12 December 2012, pages 387-398.<P> In rare event simulation, we look for estimators such that the relative accuracy of the output is ''controlled'' when the rarity is getting more and more critical. Different robustness properties have been defined...</p></i>

This paper reports simulation experiments, applying the cross entropy method suchas the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failurebiasing schemes that have been proved to give...