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

• 成果类型: Article
• 署名作者: Foondun, Mohammud; Joseph, Mathew; Kim, Kunwoo
• 署名单位: University of Strathclyde; Indian Statistical Institute; Indian Statistical Institute Bangalore; Pohang University of Science & Technology (POSTECH)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01153-w
• 发表日期: 2023
• 页码: 553-613
• 关键词: support theorem

摘要

We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Holder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Holder semi-norms.