Rhee, C., Blanchet, J., & Zwart, B. (2016). Sample Path Large Deviations for Heavy-Tailed L\’evy Processes and Random Walks. ArXiv. /abs/1606.02795

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Abstract

Let X be a Lévy process with regularly varying Lévy measure ν. We obtain sample-path large deviations of scaled processes Xn (t) X (nt)/n and obtain a similar result for random walks. Our results yield detailed asymptotic estimates in scenarios where multiple big jumps in the increment are required to make a rare event happen. In addition, we investigate connections with the classical large-deviations framework. In that setting, we show that a weak large deviations principle (with logarithmic speed) holds, but a full large-deviations principle does not hold.

Chang-Han Rhee, Jose Blanchet, Bert Zwart
Publication date
2016/6
Journal
arXiv preprint arXiv:1606.02795