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

Let uα,d=uα,dt,x, t∈0,T,x∈ℝd 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 underlyin...

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Bibliographic Details
Published in:Discrete dynamics in nature and society 2021-10, Vol.2021, p.1-17
Main Authors: Wang, Wensheng, Chang, Xiaoying, Liao, Wang
Format: Article
Language:English
Subjects:
Asymptotic properties
Fourier analysis
Gaussian process
Harmonic analysis
Noise
Parameter estimation
Random variables
Spacetime
Thermodynamics
White noise
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Summary:Let uα,d=uα,dt,x, t∈0,T,x∈ℝd 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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2021/8208934