OPTIMAL GAUSSIAN DENSITY ESTIMATES FOR A CLASS OF STOCHASTIC EQUATIONS WITH ADDITIVE NOISE

DOI10.1142/S0219025711004286zbMath1235.60060arXiv0912.3707OpenAlexW2963556658MaRDI QIDQ2996891

David Nualart, Lluís Quer-Sardanyons

Publication date: 4 May 2011

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.3707

zbMATH Keywords

Malliavin calculusstochastic partial differential equationsspatially homogeneous Gaussian noiseGaussian density estimates

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (10)

Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients ⋮ Solving a nonlinear fractional stochastic partial differential equation with fractional noise ⋮ On a class of stochastic fractional kinetic equation with fractional noise ⋮ On a nonlinear stochastic pseudo-differential equation driven by fractional noise ⋮ The density of solutions to multifractional stochastic Volterra integro-differential equations ⋮ Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension ⋮ Gaussian estimates for the solutions of some one-dimensional stochastic equations ⋮ On the density of systems of non-linear spatially homogeneous SPDEs ⋮ Density estimates and central limit theorem for the functional of fractional SDEs ⋮ The wavelet transform for Wiener functionals and some applications

Cites Work

• Stein's method on Wiener chaos
• Density formula and concentration inequalities with Malliavin calculus
• Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations
• Random nonlinear wave equations: Smoothness of the solutions
• Absolute continuity of the law of the solution to the 3-dimensional stochastic wave equation.
• A stochastic wave equation in two space dimensions: smoothness of the law
• Stochastic evolution equations with a spatially homogeneous Wiener process
• The Cauchy problem for a nonlinear stochastic wave equation in any dimension
• Existence and smoothness of the density for spatially homogeneous SPDEs
• The Malliavin Calculus and Related Topics

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