Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation. (12th October 2021)

• Record Type: Journal Article
• Authors: Wang, Wensheng; Chang, Xiaoying; Liao, Wang
• Other Names: Nurkanovic Mehmed Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2021(2021)
• Publication Date: 2021-10-12
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2021/8208934
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : Let u α, d = u α, d t, x, t ∈ 0, T, x ∈ ℝ d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process u α, d, in time, having infinite quadratic variation and dimension-dependent Gaussian asymptotic distributions. We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.