Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 11 (2006) > Paper 26 open journal systems 


On Fractional Fields indexed by Metric Spaces

Jacques Istas, Université Pierre Mendès-France


Abstract
We define and build H-fractional α-stable fields indexed by a metric space (E,d). We mainly apply these results to spheres, hyperbolic spaces and real trees


Full text: PDF

Pages: 242-251

Published on: October 11, 2006
Bibliography
  1. Bretagnolle, Jean; Dacunha-Castelle, Didier; Krivine, Jean-Louis. Lois stables et espaces $Lsp{p}$. (French) Ann. Inst. H. Poincaré Sect. B (N.S.) 2 1965/1966 231--259. MR0203757 (34 #3605)
  2. N. Chentsov. Levy's Brownian motion of several parameters and generalized white noise, Theory of Probability and its Applications 2 (1957), 265--266.
  3. Dress, Andreas; Moulton, Vincent; Terhalle, Werner. $T$-theory: an overview. European J. Combin. 17 (1996), no. 2-3, 161--175. MR1379369 (97e:05069)
  4. Faraut, Jacques; Harzallah, Khélifa. Distances hilbertiennes invariantes sur un espace homogène. (French) Ann. Inst. Fourier (Grenoble) 24 (1974), no. 3, xiv, 171--217. MR0365042 (51 #1295)
  5. Istas, Jacques. Spherical and hyperbolic fractional Brownian motion. Electron. Comm. Probab. 10 (2005), 254--262 (electronic). MR2198600
  6. Koldobskiui, A. L.. The Schoenberg problem on positive-definite functions. (Russian) Algebra i Analiz 3 (1991), no. 3, 78--85; translation in St. Petersburg Math. J. 3 (1992), no. 3, 563--570 MR1150554 (93c:42014)
  7. Koldobsky, Alexander; Lonke, Yossi. A short proof of Schoenberg's conjecture on positive definite Bull. London Math. Soc. 31 (1999), no. 6, 693--699. MR1711028 (2001j:42008)
  8. Kolmogoroff, A. N. Wienersche Spiralen und einige andere interessante Kurven im (German) C. R. (Doklady) Acad. Sci. URSS (N.S.) 26, (1940). 115--118. MR0003441 (2,220c)
  9. Lévy, Paul. Processus stochastiques et mouvement brownien. augmentée Gauthier-Villars & Cie, Paris 1965 vi+438 pp. MR0190953 (32 #8363)
  10. Maejima, Makoto. A remark on self-similar processes with stationary increments. Canad. J. Statist. 14 (1986), no. 1, 81--82. MR0839294 (87f:60080)
  11. Robertson, Guyan. Crofton formulae and geodesic distance in hyperbolic spaces. J. Lie Theory 8 (1998), no. 1, 163--172. MR1616751 (99c:53083)
  12. Robertson, Guyan; Steger, Tim. Negative definite kernels and a dynamical characterization of property Ergodic Theory Dynam. Systems 18 (1998), no. 1, 247--253. MR1609459 (99c:22008)
  13. Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932 (95f:60024)
  14. Schoenberg, I. J. Metric spaces and completely monotone functions. Ann. of Math. (2) 39 (1938), no. 4, 811--841. MR1503439
  15. Takenaka, Shigeo. Integral-geometric construction of self-similar stable processes. Nagoya Math. J. 123 (1991), 1--12. MR1126180 (93d:60070)
  16. Takenaka, Shigeo; Kubo, Izumi; Urakawa, Hajime. Brownian motion parametrized with metric space of constant Nagoya Math. J. 82 (1981), 131--140. MR0618812 (83m:60071)
  17. Valette, Alain. Les représentations uniformément bornées associées à un Bull. Soc. Math. Belg. Sér. A 42 (1990), no. 3, 747--760. MR1316222 (96i:22011a)
  18. A.Yaglom. Some classes of random fields in $n$-dimensional space, related to stationary random processes, Theory of Probability and its Applications 2 (1957), 273--320. MR94844
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X