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 , under the assumption that as , and . 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.
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”.
"Limit theorems for trawl processes." Electron. J. Probab. 26 1 - 36, 2021. https://doi.org/10.1214/21-EJP652