TY  - JOUR
ID  - Bartoszek2008
LB  - Bartoszek2008
AU  - Bartoszek, Wojciech
TI  - The work of Professor Andrzej Lasota on asymptotic stability and recent progress
ST  - The work of Professor Andrzej Lasota on asymptotic stability and recent progress
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 4
SP  - 395
EP  - 413
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.4.395
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.4.395
AB  - 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.
KW  - invariant measure
KW  - asymptotic stability
KW  - asymptotic periodicity
KW  - compact attractor
KW  - lower function
KW  - smoothing
KW  - cell cycle
KW  - sweeping
KW  - genericity
SN  - 1232-9274
ER  -