Bandt, Graf, Zaehle Fractal geometry and stochastics II

A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development. 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. The Combination Of Fractal Geometry And Stochastic Methods Can Be Used To Create Convincing Models In Many Different Areas Of Science Such As Biology, Chemistry, Computer Science, Mathematics And Physics. The Present Book Deals With The Mathematical Theory Needed For This Purpose. It Contains Contributions By Outstanding Mathematicians And Is Meant To Highlight The Principal Directions Of Research In The Field. The Contributors Were The Main Speakers At The Conference Fractal Geometry And Stochastics Ii Held At Greifswald/koserow, Germany, In August 1998. The Book Is Addressed To Mathematicians And Scientists Who Are Interested In Any Of The Following Topics: · Fractal Dimensions · Fractal Measures And Multifractals · Self-similar And Self-affine Fractals · Random Fractals · Stable Processes · Ergodic Theory And Dynamical Systems · Harmonic Analysis And Stochastic Processes On Fractals The Readers Will Be Introduced To The Most Recent Results And Problems On These Subjects And Also Be Treated To An Overview Of Their Historical Development. Both Researchers And Graduate Students Will Benefit From The Clear Expositions. Christoph Bandt, Siegfried Graf, Martina Zähle, Editors. Based On A Conference Held In Greifswald/koserow, Germany, Aug. 28-sept. 2, 1998. Includes Bibliographical References.