REFERENCES
1.
M. F.
Barnsley
, S. G.
Demko
, J. H.
Elton
and J. S.
Geronimo
, Invariant measures arising from iterated function systems with place dependent probabilities
, Ann. Inst. H. Poincaré
24
, 367
–394
(1988
).2.
R. J.
Griego
and R.
Hersh
, Random evolutions, Markov chains and systems of partial differential equations
, Proc. Nat. Acad. Sci USA
62
, 305
–308
(1969
).3.
M.
Hairer
, Exponential mixing properties of stochastic PDEs through asymptotic coupling
, Probab. Theory Relat. Fields
124
, 345
–380
(2002
).4.
S.C.
Hille
, K.
Horbacz
, T.
Szarek
& H.
Wojewódka
, Limit theorems for some Markov operators
, J. Math.Anal.Appl.
443
, 385
–408
(2016
).5.
K.
Horbacz
, Invariant measures for random dynamical systems
, Dissertationes Math.
451
, (2008
).6.
K.
Horbacz
, Continuous random dynamical systems
, J. Math. Ann. Appl.
408
, 623
–637
(2013
).7.
K.
Horbacz
, T.
Szarek
, Continuous iterated function systems on Polish spaces
, Bull. Polish Acad. Sci. Math.
49
. 2
, 191
–202
(2001
).8.
K.
Horbacz
, Strong Law of large numbers for continuous random dynamical systems
, Submitted for publication
Statistics and Probability Letters
DOI (2016
).9.
J. B.
Keller
, Stochastic equations and wave propagation in random media, Proc. Sympos. Appl. Math.
16
, 1456
–1470
(1964
).10.
A.
Lasota
and M. C.
Mackey
, Cell division and the stability of cellular population
, J. Math. Biol.
38
, 241
–261
(1999
).11.
A.
Lasota
and J.
Traple
, Invariant measures related with Poisson driven stochastic differential equation
, Stochastic Process. Appl.
106
. 1
, 81
–93
(2003
).12.
A.
Lasota
and J. A.
Yorke
, Lower bound technique for Markov operators and iterated function systems
, Random Comput. Dynam.
2
, 41
–77
(1994
).13.
T.
Lipniacki
, P.
Paszek
, A.
Marciniak-Czochra
, A. R.
Brasier
, M.
Kimel
, Transcriptional stochasticity in gene expression
, J. Theor. Biol.
238
, 348
–367
(2006
).14.
M.
Maxwell
& M.
Woodroofe
, Central limit theorems for additive functionals of Markov chains
, The Annals of Probability
, 28
(2
), 713
–724
, (2000
).15.
J. J.
Tyson
and K. B.
Hannsgen
, Cell growth and division: a deterministic /probabilistic model of the cell cycle
, J.Math. Biology
26
, 465
–475
(1988
).16.
17.
I.
Werner
, Contractive Markov system
, J. London Math. Soc.
(2
) 71
, 236
–258
(2005
).
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