Jose Blanchet. Jingchen Liu. “Total variation approximations and conditional limit theorems for multivariate regularly varying random walks conditioned on ruin.” Bernoulli 20 (2) 416 – 456, May 2014. https://doi.org/10.3150/12-BEJ492
Abstract
We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach is to study the Markov process described by the random walk conditioned on hitting a rare target set. We construct a Markov chain whose transition kernel can be evaluated directly from the increment distribution of the associated random walk. This process is shown to approximate the conditional process of interest in total variation. Then, by analyzing the approximating process, we are able to obtain asymptotic conditional joint distributions and a conditional functional central limit theorem of several objects such as the time until ruin, the whole random walk prior to ruin, and the overshoot on the target set. These types of joint conditional limit theorems have been obtained …
Authors
Jose Blanchet, Jingchen Liu
Publication date
2014/5/1
Volume
20
Issue
2
Pages
416-456
