### Abstract

We consider an infinitely divisible random field in R

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.

^{d}given as an integral of akernel 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 |
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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 |
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Number | 06 |

### Keywords

- Central limit theorem
- Infinite divisibility
- Lévy-based modelling

### Cite this

Rønn-Nielsen, A., & Jensen, E. B. V. (2018).

*Central Limit Theorem for Mean and Variogram Estimators in Lévy–based Models*. Aarhus: Centre for Stochastic Geometry and Advanced Bioimaging (CSGB), Aarhus University. CSGB Research Reports, No. 06