Opuscula Math. 28, no. 4 (2008), 395-413

Opuscula Mathematica

The work of Professor Andrzej Lasota on asymptotic stability and recent progress

Wojciech Bartoszek

Abstract. The paper is devoted to Professor Andrzej Lasota's contribution to the ergodic theory of stochastic operators. We have selected some of his important papers and shown their influence on the evolution of this topic. We emphasize the role A. Lasota played in promoting abstract mathematical theories by showing their applications. The article is focused exclusively on ergodic properties of discrete stochastic semigroups $$\{P^n : n \geq 0\}$$. Nevertheless, almost all of Lasota's results presented here have their one-parameter continuous semigroup analogs.

Keywords: invariant measure, asymptotic stability, asymptotic periodicity, compact attractor, lower function, smoothing, cell cycle, sweeping, genericity.

Mathematics Subject Classification: 37A30, 47A35, 45D05, 46B42, 60J20, 92D15.

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• Wojciech Bartoszek
• Gdańsk University of Technology, Department of Mathematics, ul. Narutowicza 11/12, 80 952 Gdańsk, Poland