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3 Bulletin of the Polish Academy of Sciences. Mathematics

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Upper estimate of concentration and thin dimensions of measures

Gacki H., Lasota A., Myjak J.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

Vol. 57, no 2

149-162

We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.

Kantorovich-Rubinstein maximum principle in the stability theory of Markov semigroups

Gacki H.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 2

211-222

A new sufficient condition for the asymptotic stability of a locally Lipschitzian Markov semigroup acting on the space of signed measures. M[sig] is proved. This criterion is applied to the semigroup of Markov operators generated by a Poisson driven stochastic differential equation.

An application of the Kantorovich-Rubinstein maximum principle in the stability theory of Markov operators

Gacki H.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

215-223

We consider the asymptotic behaviour of Markov operators acting on measures, defined on a locally are [sigma]-compact metric space. We prove a new sufficient condition for the asymptotic stability of Markov operators. This condition is applied to stochastically peturbed dynamical systems, and iterated function system.