Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion

Guodong Pang, Murad S. Taqqu

doi:10.1002/hf2.10028

Nonstationary self‐similar Gaussian processes as scaling limits of power‐law shot noise processes and generalizations of fractional Brownian motion

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Guodong Pang

The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering Pennsylvania State University University Park Pennsylvania
Murad S. Taqqu

Department of Mathematics and Statistics Boston University Boston Massachusetts

書誌事項

公開日: 2019-03-13

権利情報

http://onlinelibrary.wiley.com/termsAndConditions#am
http://onlinelibrary.wiley.com/termsAndConditions#vor

DOI

10.1002/hf2.10028

公開者: Wiley

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説明

<jats:title>Abstract</jats:title><jats:p>We study shot noise processes with Poisson arrivals and nonstationary noises. The noises are conditionally independent given the arrival times, but the distribution of each noise does depend on its arrival time. We establish scaling limits for such shot noise processes in two situations: (a) the conditional variance functions of the noises have a power law and (b) the conditional noise distributions are piecewise. In both cases, the limit processes are self‐similar Gaussian with nonstationary increments. Motivated by these processes, we introduce new classes of self‐similar Gaussian processes with nonstationary increments, via the time‐domain integral representation, which are natural generalizations of fractional Brownian motions.</jats:p>