 
Summary: The Annals of Applied Probability
2005, Vol. 15, No. 2, 10471110
DOI 10.1214/105051605000000142
© Institute of Mathematical Statistics, 2005
A SURVEY OF MAXTYPE RECURSIVE
DISTRIBUTIONAL EQUATIONS
BY DAVID J. ALDOUS1 AND ANTAR BANDYOPADHYAY
University of California, Berkeley and University of Minnesota
In certain problems in a variety of applied probability settings (from
probabilistic analysis of algorithms to statistical physics), the central re
quirement is to solve a recursive distributional equation of the form
X
d
=g((i,Xi),i 1). Here (i) and g(·) are given and the Xi are indepen
dent copies of the unknown distribution X. We survey this area, emphasizing
examples where the function g(·) is essentially a "maximum" or "minimum"
function. We draw attention to the theoretical question of endogeny: in the
associated recursive tree process Xi, are the Xi measurable functions of the
innovations process (i)?
1. Introduction. Write P for the space of probability distributions on a
