Stochastic fractional heat equations driven by fractional noises
type: Item
instance of: scholarly article
title: Stochastic fractional heat equations driven by fractional noises
zbMATH Open document ID: 1393.60071
DOI: 10.1155/2015/421705
author: Xichao Sun
author: Ming Li
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: This paper is concerned with the following stochastically fractional heat equation on \((t, x) \in [0, T] \times \mathbb{R}^d\) driven by fractional noise: \(\partial u(t, x) / \partial t = \mathcal{D}_\delta^\alpha u(t, x) + W^H(t, x) \diamond u(t, x)\), where the Hurst parameter \(H = (h_0, h_1, \ldots, h_d)\) and \(\diamond\) denotes the Skorokhod integral. A unique solution of that equation in an appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and the Hölder continuity of the solution on both space and time parameters is discussed. On the other hand, the absolute continuity of the solution is also obtained.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 6926316
Wikidata QID: Q59118532
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/421705
OpenAlex ID: W1984415676
cites work: Q4233638
cites work: Q3141895
cites work: A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions
cites work: Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations
cites work: Entropy and multifractality for the myeloma multiple TET 2 gene
cites work: On the fractal geometry of DNA by the binary image analysis
cites work: Low-dosed X-ray computed tomography imaging by regularized fully spatial fractional-order Perona-Malik diffusion
cites work: External fractional-order gradient vector Perona-Malik diffusion for sinogram restoration of low-dosed X-ray computed tomography
cites work: Q3998788
cites work: A general theory of heat conduction with finite wave speeds
cites work: On heat conduction in materials with memory
cites work: Fractal first-order partial differential equations
cites work: Chance and Stability
cites work: Wavelets-computational aspects of Sterian realistic approach to uncertainty principle in high energy physics: a transient approach
cites work: Transient aspects of wave propagation connected with spatial coherence
cites work: The heat equation with Lévy noise
cites work: Fractional SPDEs driven by spatially correlated noise: existence of the solution and smoothness of its density
cites work: On a stochastic partial differential equation with a fractional Laplacian operator
cites work: On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
cites work: On a fractional SPDE driven by fractional noise and a pure jump Lévy noise in \(\mathbb{R}^d\)
cites work: Q3375714
cites work: On a jump-type stochastic fractional partial differential equation with fractional noises
cites work: On the solution process for a stochastic fractional partial differential equation driven by space-time white noise
cites work: Stochastic Calculus for Fractional Brownian Motion and Applications
cites work: The Malliavin Calculus and Related Topics
cites work: Heat equations with fractional white noise potentials
cites work: REGULARIZATION OF QUASILINEAR HEAT EQUATIONS BY A FRACTIONAL NOISE
cites work: Stochastic evolution equations with fractional Brownian motion
cites work: Stochastic heat equation driven by fractional noise and local time
cites work: The stochastic wave equation with multiplicative fractional noise: A Malliavin calculus approach
cites work: Stochastic heat equation with multiplicative fractional-colored noise
cites work: The stochastic wave equation with fractional noise: a random field approach
cites work: On a Class of Stochastic Anderson Models with Fractional Noises
cites work: STOCHASTIC CAHN–HILLIARD EQUATION WITH FRACTIONAL NOISE
cites work: Stochastic fractional Anderson models with fractional noises
cites work: On a stochastic heat equation with first order fractional noises and applications to finance
cites work: Stochastic generalized Burgers equations driven by fractional noises
cites work: Chaos expansion of heat equations with white noise potentials
cites work: Q5422575
cites work: On the martingale problem for generators of stable processes with perturbations
cites work: Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion
cites work: The high-order SPDEs driven by multi-parameter fractional noises
cites work: Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's
description: scientific article; zbMATH DE number 6926316