Intermittency for the wave and heat equations with fractional noise in time

DOI10.1214/15-AOP1005zbMath1343.60081arXiv1311.0021MaRDI QIDQ282520

Daniel Conus, Raluca M. Balan

Publication date: 12 May 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0021

zbMATH Keywords

fractional Brownian motionMalliavin calculusstochastic heat equationintermittencystochastic wave equation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (24)

Intermittency for the hyperbolic Anderson model with rough noise in space ⋮ Space-time fractional Anderson model driven by Gaussian noise rough in space ⋮ Local nondeterminism and local times of the stochastic wave equation driven by fractional-colored noise ⋮ High order Anderson parabolic model driven by rough noise in space ⋮ Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise ⋮ Moment bounds for some fractional stochastic heat equations on the ball ⋮ Law of iterated logarithms and fractal properties of the KPZ equation ⋮ Moment bounds for a generalized Anderson model with Gaussian noise rough in space ⋮ Hölder continuity for stochastic fractional heat equation with colored noise ⋮ Moment bounds of a class of stochastic heat equations driven by space-time colored noise in bounded domains ⋮ Lyapunov exponents of the SHE under general initial data ⋮ On a class of mixed stochastic heat equations driven by spatially homogeneous Gaussian noise ⋮ Fractional stochastic wave equation driven by a Gaussian noise rough in space ⋮ On a class of stochastic partial differential equations ⋮ A note on intermittency for the fractional heat equation ⋮ Temporal asymptotics for fractional parabolic Anderson model ⋮ SPDEs with colored Gaussian noise: a survey ⋮ Moment bounds and asymptotics for the stochastic wave equation ⋮ Fractional kinetic equation driven by general space-time homogeneous Gaussian noise ⋮ Lyapunov exponents of the half-line SHE ⋮ Large deviation principle for a space-time fractional stochastic heat equation with fractional noise ⋮ On weak convergence of stochastic heat equation with colored noise ⋮ Parabolic Anderson model with space-time homogeneous Gaussian noise and rough initial condition ⋮ Upper-tail large deviation principle for the ASEP

Cites Work

• Unnamed Item
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• Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise
• Solving the KPZ equation
• On the chaotic character of the stochastic heat equation. II
• On the chaotic character of the stochastic heat equation, before the onset of intermitttency
• Asymptotic behavior of the solution of heat equation driven by fractional white noise
• Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\)
• A note on intermittency for the fractional heat equation
• The stochastic wave equation with fractional noise: a random field approach
• Feynman-Kac formula for heat equation driven by fractional white noise
• The stochastic wave equation with multiplicative fractional noise: A Malliavin calculus approach
• Exponential asymptotics for time-space Hamiltonians
• Stochastic heat equation driven by fractional noise and local time
• Intermittency properties in a hyperbolic Anderson problem
• A note on a Feynman-Kac-type formula
• The non-linear stochastic wave equation in high dimensions
• Intermittence and nonlinear parabolic stochastic partial differential equations
• The stochastic wave equation in two spatial dimensions
• Absolute continuity of the law of the solution to the 3-dimensional stochastic wave equation.
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• Martingale transforms and Girsanov theorem for long-memory Gaussian processes
• A stochastic wave equation in two space dimensions: smoothness of the law
• Some non-linear s. p. d. e's that are second order in time
• Linear SPDEs driven by stationary random distributions
• Stochastic heat equation with multiplicative fractional-colored noise
• A note on an identity of the gamma function and Stirling's formula
• The 1-d stochastic wave equation driven by a fractional Brownian sheet
• Existence and smoothness of the density for spatially homogeneous SPDEs
• On the existence and position of the farthest peaks of a family of stochastic heat and wave equations
• Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
• Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1
• Asymptotics for a variant of the Mittag–Leffler function
• Fluctuation exponent of the KPZ/stochastic Burgers equation
• The Malliavin Calculus and Related Topics
• Dynamic Scaling of Growing Interfaces
• A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s
• Hölder-Sobolev regularity of the solution to the stochastic wave equation in dimension three
• Parabolic Anderson problem and intermittency
• THE STOCHASTIC WAVE EQUATION DRIVEN BY FRACTIONAL BROWNIAN NOISE AND TEMPORALLY CORRELATED SMOOTH NOISE
• Stochastic integration with respect to the fractional Brownian motion
• On the stochastic heat equation with spatially-colored random forcing
• Heavy-Tail Phenomena
• 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
• Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions

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