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

DOI10.1214/16-SSY218zbMath1365.60072arXiv1604.02918OpenAlexW3104041235MaRDI QIDQ5738843

Publication date: 13 June 2017

Full work available at URL: https://arxiv.org/abs/1604.02918

Laplace transform asymptotic analysis Riemann surface stationary distribution saddle-point method reflected Brownian motion in the quarter plane

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Queueing theory (aspects of probability theory) (60K25) Brownian motion (60J65) Compact Riemann surfaces and uniformization (30F10) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Invariant measures for infinite-dimensional dissipative dynamical systems (37L40)

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Green's functions with oblique Neumann boundary conditions in the quadrant ⋮ Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant ⋮ Stationary distributions for two-dimensional sticky Brownian motions: exact tail asymptotics and extreme value distributions ⋮ Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary ⋮ Integral expression for the stationary distribution of reflected Brownian motion in a wedge ⋮ Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process ⋮ Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

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