an:06176084
Zbl 1273.60054
Li, Hui; Tavakoli, Javad; Zhao, Yiqiang Q.
Analysis of exact tail asymptotics for singular random walks in the quarter plane
EN
Queueing Syst. 74, No. 2-3, 151-179 (2013).
00318082
2013
j
60G50 60J10 60K25
singular random walks in the quarter plane; generating functions; stationary probabilities; kernel method; asymptotic analysis; dominant singularity; exact tail asymptotics
The paper considers random walks in the quarter plane. Let \({p_{ij}},i,j = 0, \pm 1\) be transition probabilities of the walk inside the quarter plane. The walk is said to be singular if \(h(x,y) = xy\left( {\sum\limits_{i = - 1}^1 {\sum\limits_{j = - 1}^1 {{p_{i,j}}{x^i}{y^j}} - 1} } \right)\), as a polynomial of two complex variables \(x\) and \(y\), is either reducible or of degree one in at least one variable. The paper gives exact light tail asymptotics for stationary distribution for all eight possible different cases for the singular random walks.
Oleg K. Zakusilo (Ky??v)