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Function Spaces and Stochastic Processes on Fractals

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Fractal Geometry and Stochastics III

Part of the book series: Progress in Probability ((PRPR,volume 57))

Abstract

We summarize recent work on function spaces and stochastic processes on fractals. We discuss relations between various non-local Dirichlet forms on fractals whose domains are Besov spaces. The corresponding stochastic processes are jump-type processes. Results on heat kernel estimates for the processes are introduced. We will also discuss how jump processes and diffusion processes are related by observing their function spaces.

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Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Takashi Kumagai

  2. Department of Mathematics Malott Hall, Cornell University, Ithaca, NY, 14853, USA

    Takashi Kumagai

Authors
  1. Takashi Kumagai
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, 17487, Germany

    Christoph Bandt

  2. Department of Physics, University of Rome La Sapienza, Via G. Boni 20, Roma, 00162, Italy

    Umberto Mosco

  3. Mathematisches Institut, Friedrich-Schiller-Universität, Jena, 07740, Germany

    Martina Zähle

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© 2004 Springer Basel AG

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Kumagai, T. (2004). Function Spaces and Stochastic Processes on Fractals. In: Bandt, C., Mosco, U., Zähle, M. (eds) Fractal Geometry and Stochastics III. Progress in Probability, vol 57. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7891-3_14

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  • DOI: https://doi.org/10.1007/978-3-0348-7891-3_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9612-2

  • Online ISBN: 978-3-0348-7891-3

  • eBook Packages: Springer Book Archive

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