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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