We establish a connection between epidemic models on random networks with general infection times considered in Barbour and Reinert (2013) and first passage percolation. Using techniques developed inBhamidi, van derHofstad andHooghiemstra (2012), when each vertex has infinite contagious periods, we extend results on the epidemic curve in Barbour and Reinert (2013) from bounded degree graphs to ...

In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics...

The purpose of this article is to present the development of a wind farm, with a condition monitoring system (CMS) based on control charts as the algorithm, centred on a new index, to prevent soil pollution by oil spills in wind farms. To this end, temperature sensors can be considered as one of the more significant sensors to be employed in this study, because the information obtained with reg...

We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue t...

In this paper we work in the framework of a k-dimensional vector of log-linear risks. Under weak conditions on the marginal tails and the dependence structure of a vector of positive risks, we derive the asymptotic tail behaviour of the aggregated risk and present an application concerning log-normal risks with stochastic volatility.

These notes are based on the two lectures1 I gave in Stat 461, Applied Probability Models, as a substitute for Professor Cheng Ouyang. First, we cover the long-run behavior of Markov chains, in particular, the convergence to a stationary distribution. Second, an application to Markov chain Monte Carlo computation is given, namely, the construction and justification of the Metropolis–Hastings al...