Weak convergence to the fractional Brownian sheet and other two-parameter Gaussian processes.

DOI10.1016/j.spl.2003.09.001zbMath1116.60328OpenAlexW2046938879MaRDI QIDQ1423053

Maria Jolis, Xavier Bardina, Ciprian A. Tudor

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2003.09.001

zbMATH Keywords

Weak convergenceprocessFractional Brownian sheetTwo-parameter Gaussian processesTwo-parameter Poisson

Mathematics Subject Classification ID

Gaussian processes (60G15)

Related Items (17)

Hausdorff dimension of the graph of the fractional Brownian sheet ⋮ Approximation of the Rosenblatt sheet ⋮ Stability results for stochastic differential equations driven by an additive fractional Brownian sheet ⋮ Stochastic differential equations driven by an additive fractional Brownian sheet ⋮ Weak convergence of the complex fractional Brownian motion ⋮ Approximations of fractional Brownian motion ⋮ 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 ⋮ A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm ⋮ Approximation in law to the \(d\)-parameter fractional Brownian sheet based on the functional invariance principle ⋮ On a stochastic heat equation with first order fractional noises and applications to finance ⋮ \(L^p\) uniform random walk-type approximation for fractional Brownian motion with Hurst exponent \(0 < H < \frac{1}{2} \) ⋮ WEAK CONVERGENCE FOR QUASILINEAR STOCHASTIC HEAT EQUATION DRIVEN BY A FRACTIONAL NOISE WITH HURST PARAMETER H ∈ (½, 1) ⋮ Gaussian multi-self-similar random fields with distinct stationary properties of their rectangular increments ⋮ Approximation to Multifractional Riemann-Liouville Brownian Sheet ⋮ Weak convergence to Rosenblatt sheet

Cites Work

• Lectures on topics in stochastic differential equations
• Weak approximation of the Brownian sheet from a Poisson process in the plane
• Weak approximation of the Wiener process from a Poisson process: the multidimensional parameter set case
• Fractional Brownian sheet
• Weak approximation for a class of Gaussian processes
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
• Stochastic calculus with respect to Gaussian processes
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