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Ratio and Stochastic Ergodic Theorems for Superadditive Processes

Published online by Cambridge University Press:  20 November 2018

Humphrey Fong
Humphrey Fong*
Affiliation:
Bowling Green State University, Bowling Green, Ohio
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1. Introduction. Let (X, , m) be a σ-finite measure space and let T be a positive linear operator on L1 = L1(X, , m). T is called Markovian if

(1.1)

T is called sub-Markovian if

(1.2)

All sets and functions are assumed measurable; all relations and statements are assumed to hold modulo sets of measure zero.

For a sequence of L1+ functions (ƒ0, ƒ1, ƒ2, …), let

(ƒn) is called a super additive sequence or process, and (sn) a super additive sum relative to a positive linear operator T on L1 if

(1.3)

and

(1.4)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 441 - 447
Copyright
Copyright © Canadian Mathematical Society 1979

References

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