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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/8208934 |
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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. |
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| ISSN: | 1026-0226 1607-887X |