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Small-time compactness and convergence behavior of deterministically and self-normalised Lévy processes

Maller, Ross; Mason, David M.


Consider a Levy process Xt with quadratic variation process Vt = σ2t+Σ0<s≤t(ΔXs)2, t> 0, where ΔXt = Xt -Xt- denotes the jump process of ×. We give stability and compactness results, as t ↕ 0, for the convergence both of the deterministically normed (and possibly centered) processes Xt and Vt, as well as theorems concerning the "self-normalised" process Xt//√V t- Thus, we consider the stochastic compactness and convergence in distribution of the 2-vector ((Xt - a(t))/b(t),Vt/b(t)), for...[Show more]

CollectionsANU Research Publications
Date published: 2009-11-18
Type: Journal article
Source: Transactions of the American Mathematical Society
DOI: 10.1090/S0002-9947-09-05032-6


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