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2021 Limit theorems for trawl processes
Mikko S. Pakkanen, Riccardo Passeggeri, Orimar Sauri, Almut E. D. Veraart
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Electron. J. Probab. 26: 1-36 (2021). DOI: 10.1214/21-EJP652


In this work we derive limit theorems for trawl processes. First, we study the asymptotic behavior of the partial sums of the discretized trawl process (XiΔn)i=0nt1, under the assumption that as n, Δn0 and nΔnμ[0,+]. Second, we prove a general result on functional convergence in distribution of trawl processes. As an application of this result, we show that a trawl process whose Lévy measure tends to infinity converges in distribution, under suitable rescaling, to a Gaussian moving average process.

Funding Statement

R. P. acknowledges the support provided by the Fondation Sciences Mathématiques de Paris (FSMP) fellowship, held at LPSM (Sorbonne University). O. S. would like to thank the Villum Fonden for providing partial funding for this research as part of the project number 11745 titled “Ambit Fields: Probabilistic Properties and Statistical Inference”.


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Mikko S. Pakkanen. Riccardo Passeggeri. Orimar Sauri. Almut E. D. Veraart. "Limit theorems for trawl processes." Electron. J. Probab. 26 1 - 36, 2021.


Received: 28 October 2020; Accepted: 22 May 2021; Published: 2021
First available in Project Euclid: 13 September 2021

arXiv: 2009.10698
Digital Object Identifier: 10.1214/21-EJP652

Primary: 60F17
Secondary: 60G10 , 60G57

Keywords: Functional limit theorem , moving average , partial sum , stable convergence , trawl process


Vol.26 • 2021
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