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

Abstract

Let $V_t$ be a driftless subordinator, and let denote $m_t^{(1)}\ge m_t^{(2)}\ge \dots$ its jump sequence on interval $[0,t]$. Put $V_t^{(k)}=V_t-m_t^{(1)}-\dots -m_t^{(k)}$ 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 $t\downarrow 0$ or $t\to \infty$.

14 pages

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