Annals of Probability
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We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on Rd (∂∂t−12Δ)u(t,x)=ρ(u(t,x))M˙(t,x), for measure-valued initial data, where M˙ is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. ... (See full text for complete abstract)
Stochastic heat equation; Parabolic Anderson model; Space-time Hölder regularity; Spatially homogeneous noise; Comparison principle; Measure-valued initial data
Comparison Principle for Stochastic Heat Equation on Rd.
Annals of Probability, 47(2),