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2017 Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach
Sandro Franceschi, Irina Kourkova
Stoch. Syst. 7(1): 32-94 (2017). DOI: 10.1214/16-SSY218

Abstract

Brownian motion in $\mathbf{R}_{+}^{2}$ with covariance matrix $\Sigma$ and drift $\mu$ in the interior and reflection matrix $R$ from the axes is considered. The asymptotic expansion of the stationary distribution density along all paths in $\mathbf{R}_{+}^{2}$ is found and its main term is identified depending on parameters $(\Sigma,\mu,R)$. 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 $\mathbf{Z}_{+}^{2}$ with jumps to the nearest-neighbors in the interior is developed in this article for diffusion processes on $\mathbf{R}_{+}^{2}$ with reflections on the axes.

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Sandro Franceschi. Irina Kourkova. "Asymptotic expansion of stationary distribution for reflected Brownian motion in the quarter plane via analytic approach." Stoch. Syst. 7 (1) 32 - 94, 2017. https://doi.org/10.1214/16-SSY218

Information

Received: 1 April 2016; Published: 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1365.60072
MathSciNet: MR3663338
Digital Object Identifier: 10.1214/16-SSY218

Subjects:
Primary: 05A15 , 37L40 , 60J65
Secondary: 30D05 , 30F10 , 60K25

Keywords: asymptotic analysis , Laplace transform , Reflected Brownian motion in the quarter plane , Riemann surface , saddle-point method , stationary distribution

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Vol.7 • No. 1 • 2017
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