#### Örjan Stenflo's thesis: Ergodic theorems for iterated function
systems controlled by stochastic sequences

#### (Doctoral thesis No 14 (ISBN 91-7191-451-X). Defended in May 1998
at Umeå University, Sweden. Thesis advisors: Dmitrii Silvestrov
and Hans
Wallin.)

Abstract (4 pages)

Introduction (18 pages) An
introduction to the thesis topic; (Limit theorems for stochastic
sequences arising from random iterations of functions.) Related results
can be found within the theory of fractals, stochastically recursive
sequences, random systems with complete connections, Iterated Function
Systems, discrete time Markov processes, learning models, dynamical
systems, non-linear time series etc. ) This paper contains no new
results but gives a survey of the literature and also in particular a
survey of the contents of papers A-E listed below.

Paper A (9 pages) (Iterated Function
Systems Controlled by a Semi-Markov Chain. Published in Theory
Stochastic Process., **18** (1996), no. 1-2, 305-313.)

Paper B (20 pages) (Ergodic Theorems for
Iterated Function Systems Controlled by Regenerative Sequences.
Published in J. Theoret. Probab. **11** (1998), no. 3, 589-608.
Joint paper with Dmitrii Silvestrov.)

Paper C (18 pages) (Ergodic Theorems for
Markov chains represented by Iterated Function Systems. A revised version of this paper was published in
Bull. Polish Acad. Sci. Math., **49** (2001), no. 1, 27-43.)

Paper D (12 pages) (Ergodic Theorems for
Iterated Function Systems with Time Dependent Probabilities. Published
in Theory Stochastic Process., **19** (1997), no. 3-4, 436-446.)

Paper E (9 pages) (Ergodic Theorems for
Time-Dependent Random Iteration of Functions. Published in Fractals and
Beyond: Complexities in the Sciences, M. M. Novak (ed.), World
Scientific, 1998, 129-136.)

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