A probabilistic look at the Wiener-Hopf equation

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

spread-out distribution

renewal equation

random walk

Lindley equation

ladder heights

integral equation

first passage time

exponential change of measure

subexponential distribution

coupling

supermartingale

Publication and Content Type

art (subject category)

ref (subject category)