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\(\delta \)-Records Observations in Models with Random Trend

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The Mathematics of the Uncertain

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 142))

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Abstract

In this paper we prove a Law of Large Numbers for the number of \(\delta \)-records in a sequence of random variables with an underlying trend. Our results generalizes results appeared in the literature for the i.i.d. case and for records in models with random trend. Two examples to illustrate the application of our results are included.

This work is dedicated to the memory of Pedro Gil, who his students, colleagues and friends will miss. For all those who were lucky enough to know him, his professional career and his excellent human quality leave a difficult space to fill.

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Acknowledgements

Support from Grant MTM2014-53340-P of MINECO is gratefully acknowledged. The authors are members of the research group “Modelos Estocásticos”, supported by DGA and the European Social Fund.

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Authors and Affiliations

  1. Departamento Ingeniería Matemática y Centro de Modelamiento Matemático (UMI 2807, CNRS), Universidad de Chile, Santiago, Chile

    Raúl Gouet

  2. Facultad de Ciencias, Departamento de Métodos Estadísticos and BIFI, Universidad de Zaragoza, Zaragoza, Spain

    Miguel Lafuente, F. Javier López & Gerardo Sanz

Authors
  1. Raúl Gouet
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  2. Miguel Lafuente
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  3. F. Javier López
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  4. Gerardo Sanz
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Corresponding author

Correspondence to Miguel Lafuente .

Editor information

Editors and Affiliations

  1. Liberbank, Oviedo, Spain

    Eduardo Gil

  2. Viajes El Corte Inglés, Oviedo, Spain

    Eva Gil

  3. Funl Media, Oxford, United Kingdom

    Juan Gil

  4. Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain

    María Ángeles Gil

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Gouet, R., Lafuente, M., Javier López, F., Sanz, G. (2018). \(\delta \)-Records Observations in Models with Random Trend. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_20

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  • DOI: https://doi.org/10.1007/978-3-319-73848-2_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73847-5

  • Online ISBN: 978-3-319-73848-2

  • eBook Packages: EngineeringEngineering (R0)

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