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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/86

Title: Asymptotic behaviour of Wiener-Hopf factors of a random walk
Authors: VERAVERBEKE, Noel
Keywords: Stochastic processes
Issue Date: 1977
Citation: Stoch. Processes Appl.; 5(1), p27-37
Abstract: For a random walk governed by a general distribution function F on (−∞, +∞), we establish the exponential and subexponential asymptotic behaviour of the corresponding right Wiener-Hopf factor F+. The results apply to classes of distribution functions in recent publications: the subexponential class Image and a related (exponential) class Imageγ. Given the behaviour of F+, the Wiener-Hopf identity is used, to obtain the behaviour of F. To reverse the argument, we derive a new identity, similar in form to the first one. The results for F+ are then fruitfully applied to give a full description of the tail behaviour of the maximum of the randon walk. Also they provide new proofs for recent theorems on the tail of the waiting-time distribution in the GI/G/1 queue.
URI: http://hdl.handle.net/1942/86
DOI: 10.1016/0304-4149(77)90047-3
Type: Journal Contribution
Appears in Collections: Research publications

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