A large deviation principle for the stochastic heat equation with general rough noise

2022/05/26 by Ruinan Li, Ran Wang, Li, Ruinan +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Primary 60F10 #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #secondary 60H15

paper · pdf · doi:10.48550/arxiv.2205.13157

openalex publication_date 2022/05/26 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

We study Freidlin-Wentzell's large deviation principle for one dimensional nonlinear stochastic heat equation driven by a Gaussian noise: (∂ u^ε(t,x))/(∂ t) = (∂² u^ε(t,x))/(∂ x²)+√(ε) σ(t, x, u^ε(t,x))W(t,x), tgt; 0, x∈ℝ, where W is white in time and fractional in space with Hurst parameter H∈(\frac 14,\frac 12). Recently, Hu and Wang (\it Ann. Inst. Henri Poincaré Probab. Stat. \bf 58 (2022) 379-423) studied the well-posedness of this equation without the technical condition of σ(0)=0 which was previously assumed in Hu et al. (\it Ann. Probab. \bf 45 (2017) 4561-4616). We adopt a new sufficient condition proposed by Matoussi et al. (\it Appl. Math. Optim. 83 (2021) 849-879) for the weak convergence criterion of the large deviation principle.

Related

• A large deviation principle for nonlinear stochastic wave equation driven by rough noise
• Large deviations for a spatial average of stochastic heat and wave equations
• Moderate deviations for a fractional stochastic heat equation with spatially correlated noise
• Large deviations for stochastic heat equations with memory driven by\n Levy-type noise
• Large deviation principle for certain spatially lifted Gaussian rough path