Comparison principle for stochastic heat equation on ℝ^d

2016/07/14 by Le Chen, Chen, Le, Jingyu Huang +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1607.03998

openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the strong comparison principle and strict positivity of 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), for measure-valued initial data, where M is a spatially homogeneous Gaussian noise that is white in time and ρ is Lipschitz continuous. These results are obtained under the condition that ∫_ℝ^d(1+|ξ|²)^α-1f(d ξ)0.

Citations

• Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency
• Parabolic Anderson Model with space-time homogeneous Gaussian noise and rough initial condition

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