Convergence to stable limits for ratios of trimmed Levy processes and\n their jumps

2017/08/25 by Yuguang Ipsen, Ipsen, Yuguang F., Péter Kevei +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1708.08344

openalex publication_date 2017/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive characteristic function identities for conditional distributions of\nan r-trimmed Levy process given its r largest jumps up to a designated time t.\nAssuming the underlying Levy process is in the domain of attraction of a stable\nprocess as t goes to 0, these identities are applied to show joint convergence\nof the trimmed process divided by its large jumps to corresponding quantities\nconstructed from a stable limiting process. This generalises related results in\nthe 1-dimensional subordinator case developed in Kevei & Mason (2014) and\nproduces new discrete distributions on the infinite simplex in the limit.\n

Citations

• The limit distribution of ratios of jumps and sums of jumps of subordinators
• Negative Binomial Construction of Random Discrete Distributions on the Infinite Simplex

Cited by

• Limit Theorems for the Pitman-Yor Frequency Spectrum

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