Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise

DOI10.1007/s00440-017-0783-zzbMath1391.60153arXiv1602.05617OpenAlexW2963777848MaRDI QIDQ1647934

David Nualart, Yaozhong Hu, Le Chen, Kamran Kalbasi

Publication date: 27 June 2018

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.05617

zbMATH Keywords

Lyapunov exponentsstochastic heat equationfractional calculusFeynman-Kac formulaintermittencymoment boundsFeynman-Kac integraltime fractional Gaussian noise

Mathematics Subject Classification ID

Random fields (60G60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (14)

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 ⋮ Precise moment asymptotics for the stochastic heat equation of a time-derivative Gaussian noise ⋮ Joint Hölder continuity of parabolic Anderson model ⋮ Some recent progress on stochastic heat equations ⋮ Parabolic Anderson model with a fractional Gaussian noise that is rough in time ⋮ Feynman–Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise ⋮ Lyapunov exponents of the SHE under general initial data ⋮ Solvability of parabolic Anderson equation with fractional Gaussian noise ⋮ Intermittency for the parabolic Anderson model of Skorohod type driven by a rough noise ⋮ Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise ⋮ Moderate deviations for stochastic heat equation with rough dependence in Space ⋮ Parabolic Anderson model with rough or critical Gaussian noise ⋮ On A Priori Estimates for Rough PDEs

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Intermittency for the wave and heat equations with fractional noise in time
• On the chaotic character of the stochastic heat equation. II
• Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\)
• Stochastic heat equation driven by fractional noise and local time
• Fractional martingales and characterization of the fractional Brownian motion
• Intermittence and nonlinear parabolic stochastic partial differential equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
• Feynman-Kac representation for the parabolic Anderson model driven by fractional noise
• Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
• Analysis on Gaussian Spaces
• The Malliavin Calculus and Related Topics
• Parabolic Anderson problem and intermittency
• Nonlinear Young integrals and differential systems in Hölder media
• Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
• Moments and growth indices for the nonlinear stochastic heat equation with rough initial conditions

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