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Probability density function of the local score position

Author

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  • Lagnoux, Agnès
  • Mercier, Sabine
  • Vallois, Pierre

Abstract

We calculate the probability density function of the local score position on complete excursions of a reflected Brownian motion. We use the trajectorial decomposition of the standard Brownian bridge to derive two different expressions of the density: the first one is based on a series and an integral while the second one is free off the series.

Suggested Citation

  • Lagnoux, Agnès & Mercier, Sabine & Vallois, Pierre, 2019. "Probability density function of the local score position," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3664-3689.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3664-3689
    DOI: 10.1016/j.spa.2018.10.008
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    References listed on IDEAS

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    1. Daudin, Jean-Jacques & Etienne, Marie Pierre & Vallois, Pierre, 2003. "Asymptotic behavior of the local score of independent and identically distributed random sequences," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 1-28, September.
    2. Chabriac, Claudie & Lagnoux, Agnès & Mercier, Sabine & Vallois, Pierre, 2014. "Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4202-4223.
    3. Claudie Hassenforder & Sabine Mercier, 2007. "Exact Distribution of the Local Score for Markovian Sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 741-755, December.
    4. Guedj Mickael & Robelin David & Hoebeke Mark & Lamarine Marc & Wojcik Jérôme & Nuel Gregory, 2006. "Detecting Local High-Scoring Segments: a First-Stage Approach for Genome-Wide Association Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-18, September.
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    Cited by:

    1. Sabine Mercier & Grégory Nuel, 2022. "Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1411-1438, September.

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    1. Sabine Mercier & Grégory Nuel, 2022. "Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1411-1438, September.
    2. M. P. Etienne & P. Vallois, 2004. "Approximation of the Distribution of the Supremum of a Centered Random Walk. Application to the Local Score," Methodology and Computing in Applied Probability, Springer, vol. 6(3), pages 255-275, September.
    3. Chabriac, Claudie & Lagnoux, Agnès & Mercier, Sabine & Vallois, Pierre, 2014. "Elements related to the largest complete excursion of a reflected BM stopped at a fixed time. Application to local score," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4202-4223.
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