On Besov regularity and local time of the stochastic heat equation

2020/06/07 by Brahim Boufoussi, Boufoussi, Brahim, Yassine Nachit +1
Economics, Econometrics and Finance · Engineering · Mathematics · #60G15 #60G17 #60H05 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2006.04235

openalex publication_date 2020/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Sharp Besov regularities in time and space variables are investigated for (u(t,x), t∈ [0,T], x∈ ℝ), the mild solution to the stochastic heat equation driven by space-time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for u(t,x) viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding level sets are also obtained.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Related

• On the uniform Besov regularity of local times of general processes
• Local times for systems of non-linear stochastic heat equations
• Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions
• Sharp Space-Time Regularity of the Solution to Stochastic Heat Equation Driven by Fractional-Colored Noise
• Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution