Stability Estimates of Markov Semigroups on Abstract States Spaces

被引:2
作者
Erkursun-ozcan, Nazife [1 ]
Mukhamedov, Farrukh [2 ]
机构
[1] Hacettepe Univ, Fac Sci, Dept Math, TR-06800 Ankara, Turkey
[2] United Arab Emirates Univ, Coll Sci, Math Sci Dept, Al Ain 15551, U Arab Emirates
关键词
Uniform asymptotically stable; C-0-Markov semigroup; ergodicity coefficient; perturbation bound; ORDERED BANACH-SPACES; ERGODICITY; CONVERGENCE; CHAINS; OPERATORS;
D O I
10.1007/s00009-020-1475-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, the stability and perturbation estimates for Markov C0-semigroups on abstract state spaces are explored using the Dobrushin ergodicity coefficient. Consequently, a linear relation between the stability of the semigroup and the sensitivity of its fixed point is obtained with respect to the perturbations of the semigroup. This investigation has led to the discovery of perturbation estimates for the time averages of uniform asymptotically stable semigroups. This work also proves the equivalence of uniform and weak ergodicities of time averages of C0-Markov semigroups in terms of the ergodicity coefficient, which shines new light on this topic. Finally, in terms of weighted averages, the unique ergodicity of semigroups is also studied. Emphasis is laid on the newly obtained results, which are new discoveries in the classical and non-commutative settings.
引用
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页数:25
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