The limit distribution of ratios of jumps and sums of jumps of subordinators

2014/07/11 by Péter Kevei, Kevei, Péter, Mason, David M. · 2 citations
Economics, Econometrics and Finance · Mathematics · #60F05 #60G51 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.3142

openalex publication_date 2014/07/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let V_t be a driftless subordinator, and let denote m_t⁽¹⁾ ≥ m_t⁽²⁾ ≥… its jump sequence on interval [0,t]. Put V_t^(k) = V_t - m_t⁽¹⁾ - …- m_t^(k) for the k-trimmed subordinator. In this note we characterize under what conditions the limiting distribution of the ratios V_t^(k) / m_t^(k+1) and m_t^(k+1) / m_t^(k) exist, as t \downarrow0 or t →∞.

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