Asymptotic Distributions for Power Variation of the Solution to a Stochastic Heat Equation

• 作者: Wen Sheng WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（9）
• 页码范围: 1367-1383
• 页数: 17页
• 语种: 英文

摘要

Let u ={u(t,x),t ∈[0,T],x ∈ R} be a solution to a stochastic heat equation driven by a space-time white noise.We study that the realized power variation of the process u with respect to the time,properly normalized,has Gaussian asymptotic distributions.In particular,we study the realized power variation of the process u with respect to the time converges weakly to Brownian motion.