Limit theorems for trawl processes
File(s)
Published version
Author(s)
Pakkanen, Mikko S
Passeggeri, Riccardo
Sauri, Orimar
Veraart, Almut ED
Type
Journal Article
Abstract
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 (Xi∆n
)
bntc−1
i=0 , under the assumption that as n ↑ ∞,
∆n ↓ 0 and n∆n → µ ∈ [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
L´evy measure tends to infinity converges in distribution, under suitable rescaling, to a Gaussian moving
average process.
of the partial sums of the discretized trawl process (Xi∆n
)
bntc−1
i=0 , under the assumption that as n ↑ ∞,
∆n ↓ 0 and n∆n → µ ∈ [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
L´evy measure tends to infinity converges in distribution, under suitable rescaling, to a Gaussian moving
average process.
Date Issued
2021-09-13
Date Acceptance
2021-05-22
Citation
Electronic Journal of Probability, 2021, 26, pp.1-36
ISSN
1083-6489
Publisher
Institute of Mathematical Statistics
Start Page
1
End Page
36
Journal / Book Title
Electronic Journal of Probability
Volume
26
Copyright Statement
© 2021 The Author(s). Creative Commons Attribution 4.0 International License.
License URL
Identifier
http://arxiv.org/abs/2009.10698v1
Subjects
math.PR
math.PR
0104 Statistics
0105 Mathematical Physics
Statistics & Probability
Publication Status
Published
Date Publish Online
2021-09-13