A probabilistic look at the Wiener-Hopf equation

Sören Asmussen

Research output: Contribution to journalArticlepeer-review

16 Citations (SciVal)

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.
Original languageEnglish
Pages (from-to)189-201
JournalSIAM Review
Volume40
Issue number2
DOIs
Publication statusPublished - 1998

Subject classification (UKÄ)

  • Probability Theory and Statistics

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

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