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Non-asymptotic statistical test of the diffusion coefficient of stochastic differential equations

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  • معلومة اضافية
    • Contributors:
      EA2151 Laboratoire de Mathématiques d'Avignon (LMA); Avignon Université (AU); Laboratoire Jean Alexandre Dieudonné (LJAD); Université Nice Sophia Antipolis (1965 - 2019) (UNS)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UniCA); Statistique pour le Vivant et l’Homme (SVH); Laboratoire Jean Kuntzmann (LJK); Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ); Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ); Université Grenoble Alpes (UGA); ANR-19-P3IA-0003,MIAI,MIAI @ Grenoble Alpes(2019); ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011); ANR-15-IDEX-0001,UCA JEDI,Idex UCA JEDI(2015); ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019); ANR-19-CE40-0024,ChaMaNe,Enjeux mathématiques issus des neurosciences(2019)
    • بيانات النشر:
      HAL CCSD
      Elsevier
    • الموضوع:
      2024
    • Collection:
      Université d'Avignon et des Pays de Vaucluse: HAL
    • نبذة مختصرة :
      International audience ; We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval [0, T] sampled with a time step ∆. Our main contribution is to control the test Type I and Type II errors in a non asymptotic setting, i.e. when the number of observations and the time step are fixed. The test statistics are calculated from the process increments. In dimension 1, the density of the test statistic is explicit. In dimension 2, the test statistic has no explicit density but upper and lower bounds are proved. We also propose a multiple testing procedure in dimension greater than 2. Every test is proved to be of a given non-asymptotic level and separability conditions to control their power are also provided. A numerical study illustrates the properties of the tests for stochastic processes with known or estimated drifts.
    • Relation:
      hal-04167385; https://hal.science/hal-04167385; https://hal.science/hal-04167385v2/document; https://hal.science/hal-04167385v2/file/main_arxiv.pdf
    • الرقم المعرف:
      10.1016/j.spa.2024.104372
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.9462A628