Convergence of trimmed Lévy processes to trimmed stable random variables at 0

Yuguang Fan

Stochastic Processes and their Applications, 2015, vol. 125, issue 10, 3691-3724

Abstract: Let (r,s)Xt be the Lévy process Xt with r largest jumps and s smallest jumps up till time t deleted and let (r)X˜t be Xt with r largest jumps in modulus up till time t deleted. We show that ((r,s)Xt−at)/bt or ((r)X˜t−at)/bt converges to a proper nondegenerate nonnormal limit distribution as t↓0 if and only if (Xt−at)/bt converges as t↓0 to an α-stable random variable, with 0<α<2, where at and bt>0 are nonstochastic functions in t. Together with the asymptotic normality case treated in Fan (2015) [7], this completes the domain of attraction problem for trimmed Lévy processes at 0.

Keywords: Lévy process; Trimming; Domain of attraction; Small times (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.04.005

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