The stochastic wave equation with fractional noise: a random field approach

DOI10.1016/j.spa.2010.08.006zbMath1202.60095arXiv0912.3865OpenAlexW2146276429MaRDI QIDQ608222

Ciprian A. Tudor, Raluca M. Balan

Publication date: 25 November 2010

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3865

zbMATH Keywords

fractional Brownian motionstochastic wave equationspatially homogeneous Gaussian noiserandom field solution

Mathematics Subject Classification ID

Stochastic integrals (60H05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise ⋮ Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise ⋮ Intermittency for the wave and heat equations with fractional noise in time ⋮ Local nondeterminism and local times of the stochastic wave equation driven by fractional-colored noise ⋮ Fractional stochastic Volterra equation perturbed by fractional Brownian motion ⋮ Approximations for a solution to stochastic heat equation with stable noise ⋮ Stochastic wave equation in a plane driven by spatial stable noise ⋮ On a class of stochastic fractional kinetic equation with fractional noise ⋮ Stochastic fractional heat equations driven by fractional noises ⋮ Newton's method for nonlinear stochastic wave equations ⋮ Sample paths of the solution to the fractional-colored stochastic heat equation ⋮ Linear SPDEs driven by stationary random distributions ⋮ Existence and regularity results for semilinear stochastic time-tempered fractional wave equations with multiplicative Gaussian noise and additive fractional Gaussian noise ⋮ Wave equation with a stochastic measure ⋮ A nonlinear wave equation with fractional perturbation ⋮ On a nonlinear stochastic pseudo-differential equation driven by fractional noise ⋮ Stochastic elastic equation driven by multiplicative multi-parameter fractional noise ⋮ On a fractional SPDE driven by fractional noise and a pure jump Lévy noise in \(\mathbb{R}^d\) ⋮ The stochastic wave equation with multiplicative fractional noise: A Malliavin calculus approach ⋮ Wiener integrals with respect to the Hermite random field and applications to the wave equation ⋮ Asymptotic distributions for power variations of the solution to the spatially colored stochastic heat equation ⋮ SOME LINEAR SPDEs DRIVEN BY A FRACTIONAL NOISE WITH HURST INDEX GREATER THAN 1/2 ⋮ Wave equation with a stable noise ⋮ Stochastic elastic equation driven by fractional Brownian motion ⋮ The linear stochastic heat equation with Hermite noise ⋮ Hitting times for the stochastic wave equation with fractional colored noise ⋮ Fractional stochastic heat equation with piecewise constant coefficients ⋮ Generalized \(k\)-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus ⋮ Anisotropic Gaussian random fields: criteria for hitting probabilities and applications ⋮ Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs ⋮ Wavelet analysis for the solution to the wave equation with fractional noise in time and white noise in space ⋮ Recent developments on stochastic heat equation with additive fractional-colored noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mild solutions for a class of fractional SPDEs and their sample paths
• A series expansion of fractional Brownian motion
• Variational solutions for partial differential equations driven by a fractional noise
• Young integrals and SPDEs
• Stochastic heat equation driven by fractional noise and local time
• The fractional stochastic heat equation on the circle: Time regularity and potential theory
• The non-linear stochastic wave equation in high dimensions
• Random nonlinear wave equations: Smoothness of the solutions
• Integration with respect to fractal functions and stochastic calculus. I
• Differential equations driven by rough signals
• Stochastic analysis of the fractional Brownian motion
• The stochastic wave equation in two spatial dimensions
• Long time existence for the wave equation with a noise term
• Study of a SPDE driven by a Poisson noise
• Evolution equations driven by a fractional Brownian motion
• Stochastic evolution equations with fractional Brownian motion
• Absolute continuity of the law of the solution to the 3-dimensional stochastic wave equation.
• A stochastic wave equation in dimension 3: Smoothness of the law
• Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
• Integration questions related to fractional Brownian motion
• Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
• A stochastic wave equation in two space dimensions: smoothness of the law
• Stochastic heat equation with multiplicative fractional-colored noise
• On Markov property of Lévy waves in two dimensions
• The 1-d stochastic wave equation driven by a fractional Brownian sheet
• Existence and smoothness of the density for spatially homogeneous SPDEs
• Stochastic calculus for fractional Brownian motion and related processes.
• Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations
• The Malliavin Calculus and Related Topics
• Stochastic integration with respect to the fractional Brownian motion
• System Control and Rough Paths
• Malliavin Calculus with Applications to Stochastic Partial Differential Equations
• Stochastic Calculus for Fractional Brownian Motion and Applications
• Stochastic calculus with respect to Gaussian processes
• Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
• Heat equations with fractional white noise potentials
• Corrections to: Extending the martingale measure stochastic integral with applications to spatially homogeneous s. p. d. e. 's
• Stochastic Equations in Infinite Dimensions

This page was built for publication: The stochastic wave equation with fractional noise: a random field approach