On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915664994762752 |
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| author | Alghamdi, Maha Mosaad A. Olenko, Andriy |
| author_facet | Alghamdi, Maha Mosaad A. Olenko, Andriy |
| contents | This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases of classical long-range dependence and cyclic long-range dependence, respectively. Using spectral methods and asymptotic theory, it is shown that the rescaled solutions of the equations converge to spatio-temporal Gaussian random fields. The limit fields are stationary in space and non-stationary in time. The covariance and spectral structures of the resulting asymptotic random fields are provided. The paper further establishes multiscaling limit theorems for the case of regularly varying asymptotics. A numerical example illustrating the theoretical results is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09308 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions Alghamdi, Maha Mosaad A. Olenko, Andriy Probability Statistics Theory 60F05, 60H15, 60G15, 60G60 This paper investigates fractional Riesz-Bessel equations with random initial conditions. The spectra of these random initial conditions exhibit singularities both at zero frequency and at non-zero frequencies, which correspond to the cases of classical long-range dependence and cyclic long-range dependence, respectively. Using spectral methods and asymptotic theory, it is shown that the rescaled solutions of the equations converge to spatio-temporal Gaussian random fields. The limit fields are stationary in space and non-stationary in time. The covariance and spectral structures of the resulting asymptotic random fields are provided. The paper further establishes multiscaling limit theorems for the case of regularly varying asymptotics. A numerical example illustrating the theoretical results is also presented. |
| title | On asymptotic behavior of solutions to random fractional Riesz-Bessel equations with cyclic long memory initial conditions |
| topic | Probability Statistics Theory 60F05, 60H15, 60G15, 60G60 |
| url | https://arxiv.org/abs/2512.09308 |