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Title:

On non-parametric estimation of the Lévy kernel of Markov processes

Document type:
Zeitschriftenaufsatz
Author(s):
Ueltzhöfer, F.A.J.
Abstract:
We consider a recurrent Markov process which is an Itô semi-martingale. The Lévy kernel describes the law of its jumps. Based on observations X(0) , X(∆), . . . , X(n∆), we construct an estimator for the Lévy kernel’s density. We prove its consistency (as n∆ → ∞ and ∆ → 0) and a central limit theorem. In the positive recurrent case, our estimator is asymptotically normal; in the null recurrent case, it is asymptotically mixed normal. Our estimator’s rate of convergence equals the non-parame...     »
Journal title:
Stochastic Processes and their Applications
Year:
2013
Journal volume:
123
Journal issue:
10
Pages contribution:
3663–3709
Reviewed:
ja
Language:
en
Fulltext / DOI:
doi:10.1016/j.spa.2013.04.023
TUM Institution:
Lehrstuhl für Mathematische Statistik
Format:
Text
 BibTeX