Stochastic comparisons for stochastic heat equation

2019/12/11 by Chen, Le, Kim, Kunwoo
#35R60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 60H15. Secondary 60G60 #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.05350

Abstract

We establish the stochastic comparison principles, including moment comparison principle as a special case, for solutions to the following nonlinear stochastic heat equation on ℝ^d ((∂ )/(∂ t) -(1)/(2)Δ) u(t,x) = ρ(u(t,x)) M(t,x), where M is a spatially homogeneous Gaussian noise that is white in time and colored in space, and ρ is a Lipschitz continuous function that vanishes at zero. These results are obtained for rough initial data and under Dalang's condition, namely, ∫_ℝ^d(1+|ξ|²)^-1f(d ξ)

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