| Softcover ISBN: | 978-2-37905-214-9 |
| Product Code: | AST/459 |
| List Price: | $69.00 |
| AMS Member Price: | $55.20 |
| Softcover ISBN: | 978-2-37905-214-9 |
| Product Code: | AST/459 |
| List Price: | $69.00 |
| AMS Member Price: | $55.20 |
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Book DetailsAstérisqueVolume: 459; 2025; 103 ppMSC: Primary 37; Secondary 60
For random compositions of independent and identically distributed measurable maps on a Polish space, the authors study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. The authors characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems.
The authors also provide sufficient practical conditions for a random map to belong to these classes. For instance, they establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover the manifold Lebesgue almost everywhere.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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For random compositions of independent and identically distributed measurable maps on a Polish space, the authors study the existence and finitude of absolutely continuous ergodic stationary probability measures (which are, in particular, physical measures) whose basins of attraction cover the whole space almost everywhere. The authors characterize and hierarchize such random maps in terms of their associated Markov operators, as well as show the difference between classes in the hierarchy by plenty of examples, including additive noise, multiplicative noise, and iterated function systems.
The authors also provide sufficient practical conditions for a random map to belong to these classes. For instance, they establish that any continuous random map on a compact Riemannian manifold with absolutely continuous transition probability has finitely many physical measures whose basins of attraction cover the manifold Lebesgue almost everywhere.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
