The Annals of Statistics

Asymptotic Inference in Levy Processes of the Discontinuous Type

Michael G. Akritas and Richard A. Johnson

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Abstract

We establish contiguity of certain families of probability measures indexed by $T$, as $T \rightarrow \infty$, for classes of stochastic processes with stationary, independent increments whose sample paths are discontinuous. Many important consequences pertaining to properties of tests and estimates then apply. A new expression for the Radon-Nikodym derivative of these processes is obtained.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 604-614.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345464

Digital Object Identifier
doi:10.1214/aos/1176345464

Mathematical Reviews number (MathSciNet)
MR615436

Zentralblatt MATH identifier
0481.62069

JSTOR
links.jstor.org

Subjects
Primary: 62M07: Non-Markovian processes: hypothesis testing
Secondary: 62M09: Non-Markovian processes: estimation 62G99: None of the above, but in this section

Keywords
Asymptotic inference stochastic process independent increments contiguity

Citation

Akritas, Michael G.; Johnson, Richard A. Asymptotic Inference in Levy Processes of the Discontinuous Type. Ann. Statist. 9 (1981), no. 3, 604--614. doi:10.1214/aos/1176345464. https://projecteuclid.org/euclid.aos/1176345464


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