L-Kuramoto-Sivashinsky SPDEs vs. time-fractional SPIDEs: exact continuity and gradient moduli, 1/2-derivative criticality, and laws

DOI10.1016/j.jde.2017.03.027zbMath1454.60085arXiv1603.01172OpenAlexW2963211627MaRDI QIDQ526025

Hassan Allouba, Yimin Xiao

Publication date: 8 May 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01172

zbMATH Keywords

kernelGaussian random fieldsstochastic integral equationsBrownian-time processesL-Kuramoto-Sivashinsky stochastic PDEtime-fractional stochastic partial integro-differential equations

Mathematics Subject Classification ID

Probabilistic potential theory (60J45) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Transition functions, generators and resolvents (60J35) Stochastic integral equations (60H20) Fractional partial differential equations (35R11) Integral equations with miscellaneous special kernels (45H05) Random integral equations (45R05)

Related Items (5)

Variations of the solution to a fourth order time-fractional stochastic partial integro-differential equation ⋮ Long time stability of nonlocal stochastic Kuramoto-Sivashinsky equations with jump noises ⋮ Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise ⋮ Long time behavior for stochastic Burgers equations with jump noises ⋮ Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations

Cites Work

• Unnamed Item
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• Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields
• Erratum: ``A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
• Time-fractional and memoryful \(\Delta^{2^{k}}\) SIEs on \(\mathbb{R}_{+}\times\mathbb{R}^{d}\): how far can we push white noise?
• Space-time fractional stochastic partial differential equations
• L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp Hölder regularity, and Swift-Hohenberg law equivalence
• Mittag-Leffler functions and their applications
• Chung's law of the iterated logarithm for anisotropic Gaussian random fields
• A decomposition of the bifractional Brownian motion and some applications
• Computational aspects of the gravitational instability problem for a multicomponent cosmological medium
• Infinite-dimensional dynamical systems in mechanics and physics.
• Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
• A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process
• Hitting properties of a random string
• Brownian-time processes: The PDE connection and the half-derivative generator
• Hausdorff measure of trajectories of multiparameter fractional Brownian motion
• Brownian-time Brownian motion SIEs on \(\mathbb{R}_{+} \times \mathbb{R}^d\): ultra regular direct and lattice-limits solutions and fourth-order SPDEs links
• Fractal and smoothness properties of space-time Gaussian models
• Fractional time stochastic partial differential equations
• Sample path properties of bifractional Brownian motion
• On bifractional Brownian motion
• Comparing Fréchet and positive stable laws
• Stochastic solution of space-time fractional diffusion equations
• Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations
• Sample paths of the solution to the fractional-colored stochastic heat equation
• From Brownian-Time Brownian Sheet to a Fourth Order and a Kuramoto–Sivashinsky-Variant Interacting PDEs Systems
• Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
• A BROWNIAN-TIME EXCURSION INTO FOURTH-ORDER PDES, LINEARIZED KURAMOTO–SIVASHINSKY, AND BTP-SPDES ON ℝ₊ × ℝ^d
• Fractal properties of the random string processes
• An inverse problem in the theory of materials with memory
• Different types of spdes in the eyes of girsanov's theorem
• The fundamental solution of the space-time fractional diffusion equation
• SPDEs law equivalence and the compact support property: applications to the Allen–Cahn SPDE
• Limit theorems for continuous-time random walks with infinite mean waiting times
• INTERACTING TIME-FRACTIONAL AND Δ^ν PDES SYSTEMS VIA BROWNIAN-TIME AND INVERSE-STABLE-LÉVY-TIME BROWNIAN SHEETS
• Fernique-type inequalities and moduli of continuity for anisotropic Gaussian random fields
• Uniqueness in law for the Allen–Cahn SPDE via change of measure
• State-Dependent Fractional Point Processes
• Nonlinear stochastic time-fractional diffusion equations on $\mathbb {R}$: Moments, Hölder regularity and intermittency
• Markov Processes, Gaussian Processes, and Local Times
• On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin
• Stochastic models for fractional calculus

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