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 [32], 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.
Type de document :
Pré-publication, Document de travail
2016
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Contributeur : Sandro Franceschi <>
Soumis le : mercredi 27 avril 2016 - 17:06:14
Dernière modification le : vendredi 7 avril 2017 - 01:09:34
Document(s) archivé(s) le : mardi 15 novembre 2016 - 15:32:17

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  • HAL Id : hal-01295562, version 2
  • ARXIV : 1604.02918

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S Franceschi, I Kurkova. ASYMPTOTIC EXPANSION OF STATIONARY DISTRIBUTION FOR REFLECTED BROWNIAN MOTION IN THE QUARTER PLANE VIA ANALYTIC APPROACH. 2016. 〈hal-01295562v2〉

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