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A generalized Cauchy process and its application to relaxation phenomena

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JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
卷 39, 期 12, 页码 2935-2951

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IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/39/12/005

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We study some of the basic properties of a generalized Cauchy process indexed by two parameters. The application of the Lamperti transformation to the generalized Cauchy process leads to a self-similar process which preserves the long-range dependence. The asymptotic properties of spectral density of the process are derived. Possible application of this process to model relaxation phenomena is considered.

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