On the stochastic heat equation with spatially-colored random forcing

DOI10.1090/S0002-9947-2012-05616-9zbMath1274.60202arXiv1003.0348OpenAlexW1989061230MaRDI QIDQ4915340

Mohammud Foondun, Davar Khoshnevisan

Publication date: 10 April 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0348

zbMATH Keywords

stochastic heat equationLévy processLyapunov exponentintermittencyspatially-colored homogeneous noise

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

• Super-Brownian motion: Path properties and hitting probabilities
• On the structure of infinitely divisible distributions
• Polynomials of the occupation field and related random fields
• Ideas in the theory of random media
• Harmonic analysis of additive Lévy processes
• Intermittency in a catalytic random medium
• The universality classes in the parabolic Anderson model
• Stochastic variational inequalities of parabolic type
• Stochastic heat equation driven by fractional noise and local time
• A two cities theorem for the parabolic Anderson model
• The non-linear stochastic wave equation in high dimensions
• Intermittence and nonlinear parabolic stochastic partial differential equations
• The Malliavin calculus for pure jump processes and applications to local time
• Absolute continuity of infinitely divisible distributions
• Comparison methods for a class of function valued stochastic partial differential equations
• White noise driven quasilinear SPDEs with reflection
• On the \(L^p\) norms of stochastic integrals and other martingales
• Burgers-KPZ turbulence. Göttingen lectures
• On the long time behavior of the stochastic heat equation
• The stochastic wave equation in two spatial dimensions
• White noise driven SPDEs with reflection
• Dirichlet forms and symmetric Markov processes
• The stochastic Burgers equation
• Stochastic Burgers and KPZ equations from particle systems
• Exponential decay rate of survival probability in a disastrous random environment
• Packing dimension of the image of fractional Brownian motion
• Regularity and irregularity of \((1+\beta)\)-stable super-Brownian motion
• Directed polymers in a random environment: Path localization and strong disorder
• The stochastic heat equation: Feynman-Kac formula and intermittence.
• Some non-linear s. p. d. e's that are second order in time
• Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere.
• Stationary parabolic Anderson model and intermittency
• The behavior of solutions of stochastic differential inequalities
• Quenched to annealed transition in the parabolic Anderson problem
• Dynkin's isomorphism theorem and the stochastic heat equation
• On the absolute continuity of Lévy processes with drift
• Sharp estimation of the almost-sure Lyapunov exponent for the Anderson model in continuous space
• Introductory lectures on fluctuations of Lévy processes with applications.
• Radial processes
• Brownian directed polymers in random environment
• Lyapunov exponent for the parabolic Anderson model with Lévy noise
• L\({}^ p\) estimates on iterated stochastic integrals
• Asymptotics for the almost sure lyapunov exponent for the solution of the parabolic Anderson problem
• A local-time correspondence for stochastic partial differential equations
• Symmetric Measures on Cartesian Products
• Second-order hyperbolic s.p.d.e.’s driven by homogeneous Gaussian noise on a hyperplane
• 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
• Existence and Uniqueness of a Solution of a Reaction‐Diffusion Equation with Polynomial Nonlinearity and White Noise Disturbance
• A condition for absolute continuity of infinitely divisible distribution functions
• On the support of solutions to the heat equation with noise
• Existence and uniqueness of solutionsto volterra's population equation with diffusion and noise
• Potential Theory of Lévy Processes
• Parabolic Anderson problem and intermittency
• Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations
• Almost-sure exponential behavior of a stochastic anderson model with continuous space parameter
• The two-dimensional stochastic heat equation: renormalizing a multiplicative noise
• On Continuous Singular Infinitely Divisible Distribution Function
• Markov Processes, Gaussian Processes, and Local Times
• Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
• On a Necessary and Sufficient Condition That an Infinitely Divisible Distribution be Absolutely Continuous
• Sur la théorie semi-classique du potentiel pur les processus à accroissements indépendants
• On the Infinitesimal Generators of Integral Convolutions
• Analytic semigroups and optimal regularity in parabolic problems
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