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- W2188243555 abstract "In this talk, we will survey several recent developments associated with rare events. In the light-tailed setting, it has long been known that sums of Markov-dependent bounded random variables exhibit large deviations that are qualitatively similar to those arising in the iid setting. In particular, in the bounded case, the summands, conditioned on a large deviation, exhibit conspiratorial behavior in which all the summands contribute in a roughly equal way to the large deviation of the sum. However, when the summands are unbounded, we will show, via a study of the single-server queue, that the large deviations behavior can be very dierent. In the unbounded context, a large deviation for the sum can arise as a consequence of unusual behavior involving only a small fraction of all the summands. In the heavy-tailed setting, we will discuss the sharp phenomenon that arises in settings in which heavy-tailed models can be approximated by diusions. In particular, there is frequently a sharp threshold below which the tail behavior is described by diusion-scale analysis, and above which heavy tails are the dominant inuence on tail behavior; blending the two approaches yields tail approximations that are better than either one by itself. We will also discuss several heavy-tailed simulation algorithms, in the context of queues, that illustrate the promise and challenges of building eective rare-event methods in the presence of heavy tails. This talk discusses joint work with Jose Blanchet, Sean Meyn, and Mariana Olvera-Cravioto." @default.
- W2188243555 created "2016-06-24" @default.
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- W2188243555 date "2011-01-01" @default.
- W2188243555 modified "2023-09-24" @default.
- W2188243555 title "Abstracts of Plenary Talks" @default.
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