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A central limit theorem for the Euler integral of a Gaussian random field

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  • Naitzat, Gregory
  • Adler, Robert J.

Abstract

Euler integrals of deterministic functions have recently been shown to have a wide variety of possible applications, including signal processing, data aggregation and network sensing. Adding random noise to these scenarios, as is natural in the majority of applications, leads to a need for statistical analysis, the first step of which requires asymptotic distribution results for estimators. The first such result is provided in this paper, as a central limit theorem for the Euler integral of pure, Gaussian, noise fields.

Suggested Citation

  • Naitzat, Gregory & Adler, Robert J., 2017. "A central limit theorem for the Euler integral of a Gaussian random field," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2036-2067.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:6:p:2036-2067
    DOI: 10.1016/j.spa.2016.09.007
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    References listed on IDEAS

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    1. Kratz, Marie F. & León, JoséR., 1997. "Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: Crossings and extremes," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 237-252, March.
    2. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
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