Sample Path Large Deviations for L 'evy Processes and Random Walks with\n Regularly Varying Increments

2016/06/08 by Chang-Han Rhee, Rhee, Chang-Han, José Blanchet +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1606.02795

openalex publication_date 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a L 'evy process with regularly varying L 'evy measure \ν. We\nobtain sample-path large deviations for scaled processes X_n(t)\n triangleq X(nt)/n and obtain a similar result for random walks. Our results\nyield detailed asymptotic estimates in scenarios where multiple big jumps in\nthe increment are required to make a rare event happen; we illustrate this\nthrough detailed conditional limit theorems. In addition, we investigate\nconnections with the classical large deviations framework. In that setting, we\nshow that a weak large deviation principle (with logarithmic speed) holds, but\na full large deviation principle does not hold.\n

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