A survey of max-type recursive distributional equations

Preprint

20 May 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0401388

Abstract

In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d g((\xi_i,X_i),i\geq 1). Here (\xi_i) and g(\cdot) are given and the X_i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(\cdot) is essentially a ``maximum'' or ``minimum'' function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process X_i, are the X_i measurable functions of the innovations process (\xi_i)?

Keywords

RECURSIVE DISTRIBUTIONAL EQUATIONS
ANALYSIS OF ALGORITHMS
INNOVATIONS PROCESS
TYPE RECURSIVE
MAX TYPE
SURVEY

All Related Versions

Version 1, 2004-01-28, ArXiv
Version 2, 2004-07-10, ArXiv
Version 3, 2005-05-20, ArXiv
Published version: The Annals of Applied Probability, 15 (2), 1047.

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