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Central limit theorem for mean and variogram estimators in Lévy–based models

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  12 July 2019

Anders Rønn-Nielsen  and
Eva B. Vedel Jensen
Anders Rønn-Nielsen*
Affiliation:
Copenhagen Business School
Eva B. Vedel Jensen*
Affiliation:
Aarhus University
*
* Postal address: Department of Finance, Copenhagen Business School, Solbjerg Plads 3, DK–2000 Frederiksberg C, Denmark. Email address: aro.fi@cbs.dk
** Postal address: Department of Mathematics, Aarhus University, NyMunkegade 118, DK–8000 Aarhus C, Denmark. Email address: eva@math.au.dk
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Abstract

We consider an infinitely divisible random field in ℝd given as an integral of a kernel function with respect to a Lévy basis. Under mild regularity conditions, we derive central limit theorems for the moment estimators of the mean and the variogram of the field.

Keywords

Central limit theoreminfinite divisibilityLévy-based modelling

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 209 - 222
Copyright
© Applied Probability Trust 2019 

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