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Fractal Geometry and Stochastics II : Progress in Probability - Christoph Bandt

Fractal Geometry and Stochastics II

Progress in Probability

By: Christoph Bandt (Editor), Siegfried Graf (Editor), Martina Zahle (Editor), Thomas M. Liggett (Editor), Charles Newman (Editor)

Hardcover Published: 14th February 2000
ISBN: 9783764362157
Number Of Pages: 292

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The second conference on Fractal Geometry and Stochastics was held at Greifs- wald/Koserow, Germany from August 28 to September 2, 1998. Four years had passed after the first conference with this theme and during this period the interest in the subject had rapidly increased. More than one hundred mathematicians from twenty-two countries attended the second conference and most of them presented their newest results. Since it is impossible to collect all these contributions in a book of moderate size we decided to ask the 13 main speakers to write an account of their subject of interest. The corresponding articles are gathered in this volume. Many of them combine a sketch of the historical development with a thorough discussion of the most recent results of the fields considered. We believe that these surveys are of benefit to the readers who want to be introduced to the subject as well as to the specialists. We also think that this book reflects the main directions of research in this thriving area of mathematics. We express our gratitude to the Deutsche Forschungsgemeinschaft whose financial support enabled us to organize the conference. The Editors Introduction Fractal geometry deals with geometric objects that show a high degree of irregu- larity on all levels of magnitude and, therefore, cannot be investigated by methods of classical geometry but, nevertheless, are interesting models for phenomena in physics, chemistry, biology, astronomy and other sciences.

Fractal Sets and Measuresp. 1
Multifractal Geometryp. 3
Sixty Years of Bernoulli Convolutionsp. 39
Iterated Function Systemsp. 67
Problems on Self-similar Geometryp. 69
Problems on Self-similar Sets and Self-affine Sets: An Updatep. 95
Stochastic Processes, Random Fractalsp. 107
Selfsimilar Fractals and Selfsimilar Random Fractalsp. 109
Random Coverings and Multiplicative Processesp. 125
Recent Results on Mandelbrot Multiplicative Cascadesp. 147
The Weierstrass-Mandelbrot Process Provides a Series Approximation to the Harmonizable Fractional Stable Motionp. 161
Fractals and Dynamical Systemsp. 181
An Ergodic Theoretic Approach to Mean Field Coupled Mapsp. 183
Entropy and Dimension Families Associated with Equilibrium Measures for Hyperbolic Dynamical Systemsp. 209
Harmonic Analysis on Fractalsp. 225
On Limit Theorems for Brownian Motions on Unbounded Fractal Setsp. 227
Heat Kernels and Spectral Asymptotics for some Random Sierpinski Gasketsp. 239
Lagrangian Metrics and Fractal Dynamicsp. 269
List of Participantsp. 285
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764362157
ISBN-10: 3764362154
Series: Progress in Probability
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 292
Published: 14th February 2000
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.61

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