Asymptotic theory for the detection of mixing in anomalous diffusion
In this paper, we develop asymptotic theory for the mixing detection methodology proposed by Magdziarz and Weron [Phys. Rev. E 84, 051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes, including fractional Gaussian noise and the fractional Ornstein–Uhlenbeck process....
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| Veröffentlicht in: | Journal of mathematical physics 2021-06, Vol.62 (6) |
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| creator | Zhang, Kui Didier, Gustavo |
| description | In this paper, we develop asymptotic theory for the mixing detection methodology proposed by Magdziarz and Weron [Phys. Rev. E 84, 051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes, including fractional Gaussian noise and the fractional Ornstein–Uhlenbeck process. We show that the asymptotic distribution and convergence rates of the detection statistic may be, respectively, Gaussian or non-Gaussian and standard or nonstandard depending on the diffusion exponent. The results pave the way for mixing detection based on a single observed sample path and by means of robust hypothesis testing. |
| doi_str_mv | 10.1063/5.0023227 |
| format | Article |
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Rev. E 84, 051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes, including fractional Gaussian noise and the fractional Ornstein–Uhlenbeck process. We show that the asymptotic distribution and convergence rates of the detection statistic may be, respectively, Gaussian or non-Gaussian and standard or nonstandard depending on the diffusion exponent. The results pave the way for mixing detection based on a single observed sample path and by means of robust hypothesis testing.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/5.0023227</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>New York: American Institute of Physics</publisher><subject>Asymptotic methods ; Asymptotic properties ; Gaussian process ; Hypothesis testing ; Physics ; Random noise ; Stochastic processes</subject><ispartof>Journal of mathematical physics, 2021-06, Vol.62 (6)</ispartof><rights>Author(s)</rights><rights>2021 Author(s). 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Rev. E 84, 051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes, including fractional Gaussian noise and the fractional Ornstein–Uhlenbeck process. We show that the asymptotic distribution and convergence rates of the detection statistic may be, respectively, Gaussian or non-Gaussian and standard or nonstandard depending on the diffusion exponent. 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Rev. E 84, 051138 (2011)]. The assumptions cover a broad family of Gaussian stochastic processes, including fractional Gaussian noise and the fractional Ornstein–Uhlenbeck process. We show that the asymptotic distribution and convergence rates of the detection statistic may be, respectively, Gaussian or non-Gaussian and standard or nonstandard depending on the diffusion exponent. The results pave the way for mixing detection based on a single observed sample path and by means of robust hypothesis testing.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0023227</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0003-1363-5868</orcidid></addata></record> |
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| subjects | Asymptotic methods Asymptotic properties Gaussian process Hypothesis testing Physics Random noise Stochastic processes |
| title | Asymptotic theory for the detection of mixing in anomalous diffusion |
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