Approximation in law to the \(d\)-parameter fractional Brownian sheet based on the functional invariance principle

DOI10.4171/RMI/444zbMath1102.60028MaRDI QIDQ2493583

Xavier Bardina, Carme Florit

Publication date: 21 June 2006

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/41960

zbMATH Keywords

weak convergencefunctional invariance principle

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Functional limit theorems; invariance principles (60F17)

Related Items (13)

Functional limit theorems for generalized variations of the fractional Brownian sheet ⋮ Approximation of the Rosenblatt sheet ⋮ Weak convergence to a class of Gaussian proccesses in anisotropique ⋮ Approximation to two independent Gaussian processes from a unique Lévy process and applications ⋮ Linear SPDEs driven by stationary random distributions ⋮ Convergence in law to operator fractional Brownian motion of Riemann-Liouville type ⋮ Approximation of fractional Brownian sheet by Wiener integral ⋮ Weak convergence for the fourth-order stochastic heat equation with fractional noises ⋮ Weak convergence to the fractional Brownian sheet using martingale differences ⋮ Weak convergence towards two independent Gaussian processes from a unique Poisson process ⋮ Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces ⋮ Approximation to Multifractional Riemann-Liouville Brownian Sheet ⋮ Weak convergence to Rosenblatt sheet

Cites Work

• Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes.
• Convergence in law to the multiple fractional integral.
• Stochastic calculus with respect to Gaussian processes

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