Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach

Abstract : Brownian motion in R 2 + with covariance matrix Σ and drift μ in the interior and reflection matrix R from the axes is considered. The asymptotic expansion of the stationary distribution density along all paths in R 2 + is found and its main term is identified depending on parameters (Σ, μ, R). For this purpose the analytic approach of Fayolle, Iasnogorodski and Malyshev in [12] and [36], restricted essentially up to now to discrete random walks in Z 2 + with jumps to the nearest-neighbors in the interior is developed in this article for diffusion processes on R 2 + with reflections on the axes.
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Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01295562
Contributeur : Sandro Franceschi <>
Soumis le : lundi 3 avril 2017 - 21:17:03
Dernière modification le : jeudi 27 avril 2017 - 09:46:07

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  • HAL Id : hal-01295562, version 3
  • ARXIV : 1604.02918

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Sandro Franceschi, Irina Kourkova. Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach. 2016. <hal-01295562v3>

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