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On the stationary distribution of reflected Brownian motion in a non-convex wedge

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  • معلومة اضافية
    • Contributors:
      Systèmes de transport automatisés et sécurisés (ASTRA); Inria de Paris; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-VALEO; Calcul formel, mathématiques expérimentales et interactions (MATHEXP); Inria Saclay - Ile de France; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); Institut Polytechnique de Paris (IP Paris); Communications, Images et Traitement de l'Information (TSP - CITI); Institut Mines-Télécom Paris (IMT)-Télécom SudParis (TSP); Statistiques, Optimisation, Probabilités (SOP - SAMOVAR); Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR); Institut Mines-Télécom Paris (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom Paris (IMT)-Télécom SudParis (TSP); Laboratoire de Mathématiques d'Orsay (LMO); Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Institut Denis Poisson (IDP); Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS); This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under the Grant Agreement No. 759702; ANR-22-CE40-0002,RESYST,Systèmes stochastiques réfléchis(2022); European Project: 759702,COMBINEPIC
    • بيانات النشر:
      HAL CCSD
      Polymat Publishing Company
    • الموضوع:
      2021
    • Collection:
      Université d'Orléans: HAL
    • نبذة مختصرة :
      32 pages, 39 ref. ; International audience ; We study the stationary reflected Brownian motion in a non-convex wedge, which, compared to its convex analogue model, has been much rarely analyzed in the probabilistic literature. We prove that its stationary distribution can be found by solving a two dimensional vector boundary value problem (BVP) on a single curve for the associated Laplace transforms. The reduction to this kind of vector BVP seems to be new in the literature. As a matter of comparison, one single boundary condition is sufficient in the convex case. When the parameters of the model (drift, reflection angles and covariance matrix) are symmetric with respect to the bisector line of the cone, the model is reducible to a standard reflected Brownian motion in a convex cone. Finally, we construct a one-parameter family of distributions, which surprisingly provides, for any wedge (convex or not), one particular example of stationary distribution of a reflected Brownian motion.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2102.11754; info:eu-repo/grantAgreement//759702/EU/Elliptic Combinatorics: Solving famous models from combinatorics, probability and statistical mechanics, via a transversal approach of special functions/COMBINEPIC; ARXIV: 2102.11754
    • الرقم المعرف:
      10.48550/arXiv.2102.11754
    • الدخول الالكتروني :
      https://hal.science/hal-03150317
      https://hal.science/hal-03150317v3/document
      https://hal.science/hal-03150317v3/file/FFR-23.pdf
      https://doi.org/10.48550/arXiv.2102.11754
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.84613DD2