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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Stochastic Systems, INFORMS Applied Probability Society, 2017, Volume 7, Number 1 (2017), 32-94., 〈https://projecteuclid.org/euclid.ssy/1495785617〉. 〈10.1214/16-SSY218〉
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Sandro Franceschi, Irina Kourkova. Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach. Stochastic Systems, INFORMS Applied Probability Society, 2017, Volume 7, Number 1 (2017), 32-94., 〈https://projecteuclid.org/euclid.ssy/1495785617〉. 〈10.1214/16-SSY218〉. 〈hal-01295562v3〉

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