Measure Attractors and Markov Attractors

The actions induced by a random dynamical system on spaces of probability measures on the state space are investigated, and generalisations of the notion of an attractor are discussed and compared. For the particular case of a random dynamical system generated by a stochastic differential equation the notion of an attractor for the associated Markov semigroup had previously been discussed in several instances in the literature. It is re-discovered here as a special case of a more general notion of an attractor in the space of measures.


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