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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| Format: | Article |
| Language: | English |
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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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| author | Wensheng Wang Xiaoying Chang Wang Liao |
| author_facet | Wensheng Wang Xiaoying Chang Wang Liao |
| author_sort | Wensheng Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1b9841c6414c4708963f66c6695fb2f9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1b9841c6414c4708963f66c6695fb2f92025-02-03T01:25:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/82089348208934Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat EquationWensheng Wang0Xiaoying Chang1Wang Liao2School of Economics, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Economics, Hangzhou Dianzi University, Hangzhou 310018, ChinaSchool of Economics, Hangzhou Dianzi University, Hangzhou 310018, ChinaLet 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.http://dx.doi.org/10.1155/2021/8208934 |
| spellingShingle | Wensheng Wang Xiaoying Chang Wang Liao Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation Discrete Dynamics in Nature and Society |
| title | Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation |
| title_full | Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation |
| title_fullStr | Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation |
| title_full_unstemmed | Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation |
| title_short | Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation |
| title_sort | asymptotic distributions for power variations of the solution to the spatially colored stochastic heat equation |
| url | http://dx.doi.org/10.1155/2021/8208934 |
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