Asymptotic theory for estimating the parameters of a Lévy process

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Abstract

We consider consistency and asymptotic normality of maximum likelihood estimators (MLE) for parameters of a Lévy process of the discontinuous type. The MLE are based on a single realization of the process on a given interval [0, t]. Depending on properties of the Lévy measure we either consider the MLE corresponding to jumps of size greater than ε and, keeping t fixed, we let ε tend to 0, or we consider the MLE corresponding to the complete information of the realization of the process on [0, t] and let t tend to ∞. The results of this paper improve in both generality and rigor previous asymptotic estimation results for such processes.

Original languageEnglish (US)
Pages (from-to)259-280
Number of pages22
JournalAnnals of the Institute of Statistical Mathematics
Volume34
Issue number1
DOIs
StatePublished - Dec 1 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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