A strong law of large numbers for iterated functions of independent random variables

Jan Wehr

doi:10.1007/BF02183629

A strong law of large numbers for iterated functions of independent random variables

Jan Wehr

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.

Original language	English (US)
Pages (from-to)	1373-1384
Number of pages	12
Journal	Journal of Statistical Physics
Volume	86
Issue number	5-6
DOIs	https://doi.org/10.1007/BF02183629
State	Published - Mar 1997

Keywords

Disordered systems
Hierarchical models
Law of large numbers
Martingales
Self-averaging

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/BF02183629

Cite this

@article{e09b05d50cb44dfba43447f161cbfdc7,

title = "A strong law of large numbers for iterated functions of independent random variables",

abstract = "We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.",

keywords = "Disordered systems, Hierarchical models, Law of large numbers, Martingales, Self-averaging",

author = "Jan Wehr",

year = "1997",

month = mar,

doi = "10.1007/BF02183629",

language = "English (US)",

volume = "86",

pages = "1373--1384",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer",

number = "5-6",

}

TY - JOUR

T1 - A strong law of large numbers for iterated functions of independent random variables

AU - Wehr, Jan

PY - 1997/3

Y1 - 1997/3

N2 - We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.

AB - We study sequences of random variables obtained by iterative procedures, which can be thought of as nonlinear generalizations of the arithmetic mean. We prove a strong law of large numbers for a class of such iterations. This gives rise to the concept of generalized expected value of a random variable, for which we prove an analog of the classical Jensen inequality. We give several applications to models arising in mathematical physics and other areas.

KW - Disordered systems

KW - Hierarchical models

KW - Law of large numbers

KW - Martingales

KW - Self-averaging

UR - http://www.scopus.com/inward/record.url?scp=0031091627&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031091627&partnerID=8YFLogxK

U2 - 10.1007/BF02183629

DO - 10.1007/BF02183629

M3 - Article

AN - SCOPUS:0031091627

SN - 0022-4715

VL - 86

SP - 1373

EP - 1384

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

A strong law of large numbers for iterated functions of independent random variables

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this