A PROBABILISTIC LOOK AT THE WIENER-HOPF EQUATION

Authors
ASMUSSEN S
Citation
S. Asmussen, A PROBABILISTIC LOOK AT THE WIENER-HOPF EQUATION, SIAM review, 40(2), 1998, pp. 189-201
Citations number
36
Categorie Soggetti
Mathematics,Mathematics
Journal title
SIAM review → ACNP
ISSN journal
00361445
Volume
40
Issue
2
Year of publication
1998
Pages
189 - 201
Database
ISI
SICI code
0036-1445(1998)40:2<189:APLATW>2.0.ZU;2-K
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 pro babilistic methods, involving random walks, supermartingales, coupling , the Hewitt-Savage 0-1 law, ladder heights, and exponential change of measure.