Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation

被引：0

作者：

Mohammud Foondun

Mathew Joseph

Kunwoo Kim

机构：

[1] University of Strathclyde,Department of Mathematics and Statistics

[2] Stat Math unit,School of Mathematics

[3] Indian Statistical Institute,undefined

[4] Pohang University of Science and Technology (POSTECH),undefined

[5] Korea Institute for Advanced Study (KIAS),undefined

来源：

Probability Theory and Related Fields | 2023年 / 185卷

关键词：

Heat equation; White noise; Stochastic partial differential equations; Small ball; Primary 60H15; Secondary; 60G17; 60G60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider the stochastic heat equation on [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,\,1]$$\end{document} with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Hölder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Hölder semi-norms.

引用

页码：553 / 613

页数：60

共 49 条

[41] Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data
Gui, Xinping
Li, Buyang
Wang, Jilu
SCIENCE CHINA-MATHEMATICS, 2024, 67 (12) : 2873 - 2898
[42] HARNACK INEQUALITY FOR STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL NOISE WITH HURST INDEX H > 1/2
Yin, Xiuwei
Shen, Guangjun
Gao, Zhenlong
JOURNAL OF MATHEMATICAL INEQUALITIES, 2020, 14 (04): : 1113 - 1122
[43] Strong error estimates for a space-time discretization of the linear-quadratic control problem with the stochastic heat equation with linear noise
Prohl, Andreas
Wang, Yanqing
IMA JOURNAL OF NUMERICAL ANALYSIS, 2022, 42 (04) : 3386 - 3429
[44] WEAK CONVERGENCE FOR QUASILINEAR STOCHASTIC HEAT EQUATION DRIVEN BY A FRACTIONAL NOISE WITH HURST PARAMETER H ∈ (1/2,1)
El Mellali, Tarik
Ouknine, Youssef
STOCHASTICS AND DYNAMICS, 2013, 13 (03)
[45] Superconvergence in H1-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh
Feng, Xinlong
He, Ruijian
Chen, Zhangxin
NUMERICAL ALGORITHMS, 2021, 86 (01) : 357 - 395
[46] Superconvergence in H1-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh
Xinlong Feng
Ruijian He
Zhangxin Chen
Numerical Algorithms, 2021, 86 : 357 - 395
[47] Hölder estimates for the\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar \partial - equation$$ \end{document} in some domains of finite typein some domains of finite type
Estela A. Gavosto
The Journal of Geometric Analysis, 1997, 7 (4): : 593 - 609
[48] On Hölder Estimates with Loss of Order One for the ∂̄\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar {\partial }$\end{document} Equation on a Class of Convex Domains of Infinite Type in ℂ3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {C}^{3}$\end{document}
Ly Kim Ha
Acta Mathematica Vietnamica, 2019, 44 (2) : 519 - 530
[49] Hölder and Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} Estimates for the ∂¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\partial }}$$\end{document}-equation in a class of convex domains of infinite type in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}^n$$\end{document}
Ly Kim Ha
Monatshefte für Mathematik, 2019, 190 (3) : 517 - 540

← 1 2 3 4 5 →