Weak approximation of the fractional Brownian sheet from random
        walks

Wang, Zhi; Yan, Litan; Yu, Xianye

doi:10.1214/ecp.v18-2878

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2021

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 8 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As to the approximation of stochastic (partial) differential equations, see [4,5,12]. For more details on this topic, see [2,19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the weak approximation to a class of Gaussian processes

Jiang

Yang

2021

J. Appl. Probab.

View full text Add to dashboard Cite

We study, under mild conditions, the weak approximation constructed from a standard Poisson process for a class of Gaussian processes, and establish its sample path moderate deviations. The techniques consist of a good asymptotic exponential approximation in moderate deviations, the Besov–Lèvy modulus embedding, and an exponential martingale technique. Moreover, our results are applied to the weak approximations associated with the moving average of Brownian motion, fractional Brownian motion, and an Ornstein–Uhlenbeck process.

show abstract

“…As to the approximation of stochastic (partial) differential equations, see [4,5,12]. For more details on this topic, see [2,19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of the weak approximation to a class of Gaussian processes

Jiang

Yang

2021

J. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…Fractional Brownian sheets have been studied extensively as a representative of anisotropic Gaussian random fields. For more information, refer to [2,3] and [26,27]. Inspired by the study of RL-fBms and fractional Brownian sheets, Dai [8] introduced the multifractional Riemann-Liouville Brownian sheet and studied the weak limit theorem for it.…”

Section: Introductionmentioning

confidence: 99%