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Feynman-Kac Formula for Iterated Derivatives of the Parabolic Anderson Model
The purpose of this paper is to establish a Feynman-Kac formula for the moments of the iterated Malliavin derivatives of the solution to the...
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Hölder Continuity for the Parabolic Anderson Model with Space-Time Homogeneous Gaussian Noise
In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with...
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Nonlinear Stochastic Heat Equation Driven by Spatially Colored Noise: Moments and Intermittency
In this article, we study the nonlinear stochastic heat equation in the spatial domain ℝ d subject to a Gaussian noise which is white in time and...
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Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise
In this paper, we prove Talagrand’s T 2 transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise,...
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Quantitative normal approximations for the stochastic fractional heat equation
In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian...
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Central limit theorems for nonlinear stochastic wave equations in dimension three
In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some...
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The hyperbolic Anderson model: moment estimates of the Malliavin derivatives and applications
In this article, we study the hyperbolic Anderson model driven by a space-time colored Gaussian homogeneous noise with spatial dimension
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Spatial asymptotic of the stochastic heat equation with compactly supported initial data
We investigate the growth of the tallest peaks of random field solutions to the parabolic Anderson models over concentric balls as the radii approach...
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On the Necessary and Sufficient Conditions to Solve A Heat Equation with General Additive Gaussian Noise
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient...
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SPDEs
The “SPDEs” in the title is shorthand for stochastic partial differential equations or more appropriately still, stochastic partial...