Abstract
We discuss how some of the ‘big theorems’ in probabilistic theory (the renewal theorem, the ergodic theorem and the martingale convergence the orem) may be used to study the geometry of deterministic fractals, particularly those displaying some form of self-similarity. Several probabilistic methods are presented in very simple cases, with an indication of some of the recent powerful applications in more sophisticated settings.
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Falconer, K.J. (1995). Probabilistic Methods in Fractal Geometry. In: Bandt, C., Graf, S., Zähle, M. (eds) Fractal Geometry and Stochastics. Progress in Probability, vol 37. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7755-8_1
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DOI: https://doi.org/10.1007/978-3-0348-7755-8_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7757-2
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