Geodesic
Asymptotic properties of semigroups of Markov operators
Mathematica Applicanda, Tome 30 (2002) no. 44/03, pp. 39-51.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The author provides an overview of some main ideas and methods developed in the study of asymptotic behavior of Markov operators, and the following three properties of a Markov operator P are considered: (1) Asymptotic stability, (2) Asymptotic periodicity, (3) Sweeping with respect to a family A0⊂A: lim∫APnfdm=0 for all AA0 and fD. Applications of these results appear in the study of locally expanding mappings (on intervals, on the real line and on manifolds), integral operators (especially of Volterra types), dynamical systems with stochastic perturbations, and evolution equations. In an excellent book by the author and M. C. Mackey [Chaos, fractals, and noise, Second edition, Springer, New York, 1994; MR1244104], these and many more related results are presented in much more detail. The last section of the present paper concerns Markov operators acting on finite Borel measures on a Polish metric space. The author shows how this result yields insight into attractors of iterated function systems: they appear to be supports of invariant measures of corresponding Markov operators. The paper is the Wacław Sierpiński Lecture for the year 2002.
DOI : 10.14708/ma.v30i44/03.1900
Classification : 37A30 (28A80, 47A35, 47D07, 60J05)
Mots-clés : Ergodic theorems, spectral theory, Markov operators, Fractals, Discrete-time Markov processes on general state spaces 
@article{10_14708_ma_v30i44_03_1900,
     author = {Andrezj Lasota},
     title = {Asymptotic properties of semigroups of {Markov} operators},
     journal = {Mathematica Applicanda},
     pages = { 39--51},
     publisher = {mathdoc},
     volume = {30},
     number = {44/03},
     year = {2002},
     doi = {10.14708/ma.v30i44/03.1900},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v30i44/03.1900/}
}
TY  - JOUR
AU  - Andrezj Lasota
TI  - Asymptotic properties of semigroups of Markov operators
JO  - Mathematica Applicanda
PY  - 2002
SP  -  39
EP  - 51
VL  - 30
IS  - 44/03
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/ma.v30i44/03.1900/
DO  - 10.14708/ma.v30i44/03.1900
LA  - pl
ID  - 10_14708_ma_v30i44_03_1900
ER  - 
%0 Journal Article
%A Andrezj Lasota
%T Asymptotic properties of semigroups of Markov operators
%J Mathematica Applicanda
%D 2002
%P  39-51
%V 30
%N 44/03
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/ma.v30i44/03.1900/
%R 10.14708/ma.v30i44/03.1900
%G pl
%F 10_14708_ma_v30i44_03_1900
Andrezj Lasota. Asymptotic properties of semigroups of Markov operators. Mathematica Applicanda, Tome 30 (2002) no. 44/03, pp.  39-51. doi : 10.14708/ma.v30i44/03.1900. http://geodesic.mathdoc.fr/articles/10.14708/ma.v30i44/03.1900/

Cité par Sources :