Random fractals and Markov processes. (English) Zbl 1068.60092
Lapidus, Michel L. (ed.) et al., Fractal geometry and applications: A jubilee of Benoît Mandelbrot. Multifractals, probability and statistical mechanics, applications. In part the proceedings of a special session held during the annual meeting of the American Mathematical Society, San Diego, CA, USA, January 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3638-2/v.2; 0-8218-3292-1/set). Proceedings of Symposia in Pure Mathematics 72, Pt. 2, 261-338 (2004).
The object of this paper is to give an expository account of fractal properties of Markov processes. In the most part of the paper the author concentrates on recent results for sample paths of Lévy processes with an emphasis on methods that are applicable to more general Markov processes.
For related works see: S. J. Taylor [Math. Proc. Camb. Philos. Soc. 100, 383–406 (1986; Zbl 0622.60021)], J. Bertoin [“Lévy processes” (1996; Zbl 0861.60003)], K. Sato [“Lévy processes and infinitely divisible distributions” (1999; Zbl 0973.60001)].
For the entire collection see [Zbl 1055.37003].
For related works see: S. J. Taylor [Math. Proc. Camb. Philos. Soc. 100, 383–406 (1986; Zbl 0622.60021)], J. Bertoin [“Lévy processes” (1996; Zbl 0861.60003)], K. Sato [“Lévy processes and infinitely divisible distributions” (1999; Zbl 0973.60001)].
For the entire collection see [Zbl 1055.37003].
Reviewer: Gheorghe Oprişan (Bucureşti)
MSC:
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 60G17 | Sample path properties |
| 28A80 | Fractals |
| 60J60 | Diffusion processes |
| 28A78 | Hausdorff and packing measures |
