A local-time correspondence for stochastic partial differential equations

DOI10.1090/S0002-9947-2010-05017-2zbMath1225.60103arXiv0711.1913OpenAlexW2171451526MaRDI QIDQ3003609

Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart

Publication date: 27 May 2011

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

Full work available at URL: https://arxiv.org/abs/0711.1913

zbMATH Keywords

Gaussian noisestochastic heat equationlocal timesstochastic wave equationisomorphism theoremsexistence of process solutions

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Local time and additive functionals (60J55)

Related Items (21)

Estimates of blow‐up times of a system of semilinear SPDEs ⋮ On the chaotic character of the stochastic heat equation. II ⋮ Asymptotic properties of some space-time fractional stochastic equations ⋮ Weak nonmild solutions to some SPDEs ⋮ Semigroups, potential spaces and applications to (S)PDE ⋮ On the existence and position of the farthest peaks of a family of stochastic heat and wave equations ⋮ On the global maximum of the solution to a stochastic heat equation with compact-support initial data ⋮ Impacts of Gaussian noises on the blow-up times of nonlinear stochastic partial differential equations ⋮ Dynkin's isomorphism theorem and the stochastic heat equation ⋮ Fractional stochastic wave equation driven by a Gaussian noise rough in space ⋮ An asymptotic theory for randomly forced discrete nonlinear heat equations ⋮ Initial measures for the stochastic heat equation ⋮ Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains ⋮ Existence and space-time regularity for stochastic heat equations on p.c.f. fractals ⋮ On the stochastic heat equation with spatially-colored random forcing ⋮ On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian ⋮ SOME LINEAR SPDEs DRIVEN BY A FRACTIONAL NOISE WITH HURST INDEX GREATER THAN 1/2 ⋮ Dense blowup for parabolic SPDEs ⋮ Regularity of the solutions to SPDEs in metric measure spaces ⋮ Second order Lyapunov exponents for parabolic and hyperbolic Anderson models ⋮ Nonlinear noise excitation of intermittent stochastic PDEs and the topology of LCA groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The non-linear stochastic wave equation in high dimensions
• Necessary and sufficient conditions for the continuity of local time of Lévy processes
• Introduction to the theory of (non-symmetric) Dirichlet forms
• The stochastic wave equation in two spatial dimensions
• Dirichlet forms and symmetric Markov processes
• Long time existence for the wave equation with a noise term
• Regularity and irregularity of \((1+\beta)\)-stable super-Brownian motion
• 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
• A different construction of Gaussian fields from Markov chains: Dirichlet covariances.
• Potential theory for hyperbolic SPDEs.
• Second-order linear hyperbolic SPDEs driven by isotropic Gaussian noise on a sphere.
• Seminar on stochastic analysis, random fields and applications IV, Centro Stefano Franscini, Ascona, Switzerland, May 20--24, 2002. Proceedings
• Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise
• The Cauchy problem for a nonlinear stochastic wave equation in any dimension
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
• Regularity of the sample paths of a class of second-order SPDE's
• Random motion of strings and related stochastic evolution equations
• Hölder-Sobolev regularity of the solution to the stochastic wave equation in dimension three
• Existence, uniqueness and smoothnessfor a class of function valued stochastic partial differential equations
• A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
• Markov field properties of solutions of white noise driven quasi-linear parabolic pdes
• [https://portal.mardi4nfdi.de/wiki/Publication:5186512 Continuity of local times for L�vy processes]
• Markov Processes, Gaussian Processes, and Local Times
• The vibrating string forced by white noise

This page was built for publication: A local-time correspondence for stochastic partial differential equations