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|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.|
|Type: ||Journal Contribution|
|Appears in Collections: ||Research publications|
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