Approximation to two independent Gaussian processes from a unique Lévy process and applications

Wang, Jun; Xian-mei, Song; Shen, Guangjun; Yin, Xiuwei

doi:10.1080/03610926.2019.1615095

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the literature there are several paper dealing with the weak convergence to the fractional Brownian motion. In [7], [9] and [10] the authors built up the approximations using Poisson processes while in [11] the approximation sequence is based on a Lévy process On the other hand, in [3], it is proved that the family of processes…”

Section: Introductionmentioning

confidence: 99%

Weak convergence to the fractional Brownian sheet from a Lévy sheet

Bardina,

Rovira

2020

Preprint

View full text Add to dashboard Cite

In this paper, we show an approximation in law, in the space of the continuous functions on [0, 1] 2 , of two-parameter Gaussian processes that can be represented as a Wiener type integral by processes constructed from processes that converge to the Brownian sheet. As an application, we obtain a sequence of processes constructed from a Lévy sheet that converges in law towards the fractional Brownian sheet.

show abstract