Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

Anders  Rønn-Nielsen; Eva B. Vedel Jensen

Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Department of Finance

Aarhus University

Research output: Working paper › Research

Abstract

We consider an infinitely divisible random field in R^d 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.

Original language	English
Place of Publication	Aarhus
Publisher	Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University
Number of pages	16
Publication status	Published - Jun 2018

Series	CSGB Research Reports
Number	06

Keywords

Central limit theorem
Infinite divisibility
Lévy-based modelling

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https://data.math.au.dk/publications/csgb/2018/math-csgb-2018-06.pdfLicence: Unspecified

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Cite this

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title = "Central Limit Theorem for Mean and Variogram Estimators in L{\'e}vy–based Models",

abstract = "We consider an infinitely divisible random field in Rd given as an integral of akernel function with respect to a L{\'e}vy basis. Under mild regularity conditionswe derive central limit theorems for the moment estimators of the mean andthe variogram of the field.",

keywords = "Central limit theorem, Infinite divisibility, L{\'e}vy-based modelling, Central limit theorem, Infinite divisibility, L{\'e}vy-based modelling",

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AB - We consider an infinitely divisible random field in Rd given as an integral of akernel function with respect to a Lévy basis. Under mild regularity conditionswe derive central limit theorems for the moment estimators of the mean andthe variogram of the field.

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KW - Infinite divisibility

KW - Lévy-based modelling

KW - Central limit theorem

KW - Infinite divisibility

KW - Lévy-based modelling

M3 - Working paper

T3 - CSGB Research Reports

BT - Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models

PB - Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University

CY - Aarhus

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