Rare event simulation and splitting for discontinuous random variables

Ordered Random Variables from Discontinuous Distributions

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...

The splitting method in rare event simulation

Rare Event Simulation On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a char...

An overview of importance splitting for rare event simulation

Monte Carlo simulations are a classical tool to analyse physical systems. When unlikely events are to be simulated, the importance sampling technique is often used instead of Monte Carlo. Importance sampling has some drawbacks when the problem dimensionality is high or when the optimal importance sampling density is complex to obtain. In this paper, we focus on a quite novel but somehow confide...

Rare-event Simulation for Multidimensional Regularly Varying Random Walks

We consider the problem of e¢ cient estimation via simulation of …rst passage time probabilities for a multidimensional random walk with regularly varying increments. In addition of being a natural generalization of the problem of computing ruin probabilities in insurance –in which the focus is a one dimensional random walk –this problem captures important features of large deviations for multi...