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A probabilistic look at the Wiener-Hopf equation

Asmussen, Sören LU (1998) In SIAM Review 40(2). p.189-201
Abstract
Existence, uniqueness, and asymptotic properties of solutions Z to the Wiener-Hopf integral equation Z(x) = z(x) + integral(-infinity)(x) Z(x - y)F(dy), x greater than or equal to 0, are discussed by purely probabilistic methods, involving random walks, supermartingales, coupling, the Hewitt-Savage 0-1 law, ladder heights, and exponential change of measure.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
spread-out distribution, renewal equation, random walk, Lindley equation, ladder heights, integral equation, first passage time, exponential change of measure, subexponential distribution, coupling, supermartingale
in
SIAM Review
volume
40
issue
2
pages
189 - 201
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:0032097143
ISSN
0036-1445
DOI
10.1137/S0036144596303534
language
English
LU publication?
yes
id
3ba24d0b-faf2-489e-ae2c-150702b15eee (old id 1273201)
alternative location
http://www.jstor.org/stable/pdfplus/2653331.pdf
date added to LUP
2016-04-04 09:17:19
date last changed
2022-01-29 17:11:31
@article{3ba24d0b-faf2-489e-ae2c-150702b15eee,
  abstract     = {{Existence, uniqueness, and asymptotic properties of solutions Z to the Wiener-Hopf integral equation Z(x) = z(x) + integral(-infinity)(x) Z(x - y)F(dy), x greater than or equal to 0, are discussed by purely probabilistic methods, involving random walks, supermartingales, coupling, the Hewitt-Savage 0-1 law, ladder heights, and exponential change of measure.}},
  author       = {{Asmussen, Sören}},
  issn         = {{0036-1445}},
  keywords     = {{spread-out distribution; renewal equation; random walk; Lindley equation; ladder heights; integral equation; first passage time; exponential change of measure; subexponential distribution; coupling; supermartingale}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{189--201}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Review}},
  title        = {{A probabilistic look at the Wiener-Hopf equation}},
  url          = {{http://dx.doi.org/10.1137/S0036144596303534}},
  doi          = {{10.1137/S0036144596303534}},
  volume       = {{40}},
  year         = {{1998}},
}