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

Anders  Rønn-Nielsen; Eva B. Vedel Jensen

doi:10.1017/jpr.2019.14

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

Anders Rønn-Nielsen, Eva B. Vedel Jensen

Department of Finance

Research output: Contribution to journal › Journal article › Research › peer-review

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.

Original language	English
Journal	Journal of Applied Probability
Volume	56
Issue number	1
Pages (from-to)	209–222
Number of pages	14
ISSN	0021-9002
DOIs	https://doi.org/10.1017/jpr.2019.14
Publication status	Published - Mar 2019

Keywords

Central limit theorem
Inﬁnite divisibility
Lévy-based modelling

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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 a kernel function with respect to a L{\'e}vy 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 theorem, Inﬁnite divisibility, L{\'e}vy-based modelling, Central limit theorem, Inﬁnite divisibility, L{\'e}vy-based modelling",

author = "Anders R{\o}nn-Nielsen and Jensen, {Eva B. Vedel}",

year = "2019",

month = mar,

doi = "10.1017/jpr.2019.14",

language = "English",

volume = "56",

pages = "209–222",

journal = "Journal of Applied Probability",

issn = "0021-9002",

publisher = "University of Sheffield",

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AU - Jensen, Eva B. Vedel

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N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Inﬁnite divisibility

KW - Lévy-based modelling

KW - Central limit theorem

KW - Inﬁnite divisibility

KW - Lévy-based modelling

U2 - 10.1017/jpr.2019.14

DO - 10.1017/jpr.2019.14

M3 - Journal article

VL - 56

SP - 209

EP - 222

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

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