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Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation

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  • Wensheng Wang
  • Xiaoying Chang
  • Wang Liao
  • Mehmed Nurkanovic

Abstract

Let uα,d=uα,dt,x, t∈0,T,x∈℠d be the solution to the stochastic heat equations (SHEs) with spatially colored noise. We study the realized power variations for the process uα,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.

Suggested Citation

  • Wensheng Wang & Xiaoying Chang & Wang Liao & Mehmed Nurkanovic, 2021. "Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-17, October.
    • Handle: RePEc:hin:jnddns:8208934
    DOI: 10.1155/2021/8208934
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