# Constrictive Markov operators induced by Markov processes

Constrictive Markov operators induced by Markov processes Consider a constrictive Markov operator $$T:L^1(X, \Sigma , \mu ) \rightarrow L^1(X, \Sigma , \mu )$$ T : L 1 ( X , Σ , μ ) → L 1 ( X , Σ , μ ) defined on a finite measure space $$(X, \Sigma , \mu )$$ ( X , Σ , μ ) . We give a necessary and sufficient condition for a constrictive Markov operator T which is an integral operator with stochastic kernel satisfying $$T\mathbf {1}_X=\mathbf {1}_X$$ T 1 X = 1 X . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Constrictive Markov operators induced by Markov processes

, Volume 20 (2) – Sep 3, 2015
13 pages

/lp/springer_journal/constrictive-markov-operators-induced-by-markov-processes-Lm9Ub60IAI
Publisher
Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0360-6
Publisher site
See Article on Publisher Site

### Abstract

Consider a constrictive Markov operator $$T:L^1(X, \Sigma , \mu ) \rightarrow L^1(X, \Sigma , \mu )$$ T : L 1 ( X , Σ , μ ) → L 1 ( X , Σ , μ ) defined on a finite measure space $$(X, \Sigma , \mu )$$ ( X , Σ , μ ) . We give a necessary and sufficient condition for a constrictive Markov operator T which is an integral operator with stochastic kernel satisfying $$T\mathbf {1}_X=\mathbf {1}_X$$ T 1 X = 1 X .

### Journal

PositivitySpringer Journals

Published: Sep 3, 2015

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