## Electronic Communications in Probability

### Some Notes on Topological Recurrence

Niclas Carlsson

#### Abstract

We review the concept of topological recurrence for weak Feller Markov chains on compact state spaces and explore the implications of this concept for the ergodicity of the processes. We also prove some conditions for existence and uniqueness of invariant measures of certain types. Examples are given from the class of iterated function systems on the real line.

#### Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 9, 82-93.

Dates
Accepted: 9 June 2005
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ecp/1465058074

Digital Object Identifier
doi:10.1214/ECP.v10-1137

Mathematical Reviews number (MathSciNet)
MR2150697

Zentralblatt MATH identifier
1108.37008

Rights

#### Citation

Carlsson, Niclas. Some Notes on Topological Recurrence. Electron. Commun. Probab. 10 (2005), paper no. 9, 82--93. doi:10.1214/ECP.v10-1137. https://projecteuclid.org/euclid.ecp/1465058074

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