Multifractional brownian fields indexed by metric spaces with distances of negative type

Jacques Istas

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 219-223
  • ISSN: 1292-8100

Abstract

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We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.

How to cite

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Istas, Jacques. "Multifractional brownian fields indexed by metric spaces with distances of negative type." ESAIM: Probability and Statistics 17 (2013): 219-223. <http://eudml.org/doc/274353>.

@article{Istas2013,
abstract = {We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.},
author = {Istas, Jacques},
journal = {ESAIM: Probability and Statistics},
keywords = {fractional brownian motion; self-similarity; complex variations; H-sssi processes; fractional Brownian motion; -sssi processes},
language = {eng},
pages = {219-223},
publisher = {EDP-Sciences},
title = {Multifractional brownian fields indexed by metric spaces with distances of negative type},
url = {http://eudml.org/doc/274353},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Istas, Jacques
TI - Multifractional brownian fields indexed by metric spaces with distances of negative type
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 219
EP - 223
AB - We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.
LA - eng
KW - fractional brownian motion; self-similarity; complex variations; H-sssi processes; fractional Brownian motion; -sssi processes
UR - http://eudml.org/doc/274353
ER -

References

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  1. [1] B. Bekka, P. De la Harpe and A. Valette, Kazhdan’s property (T). Cambridge University Press (2008). Zbl1146.22009
  2. [2] A. Benassi, S. Jaffard and D. Roux, Gaussian processes and pseudodifferential elliptic operators. Rev. Mat. Iberoam.13 (1997) 19–90. Zbl0880.60053MR1462329
  3. [3] A. Benassi, S. Cohen and J. Istas, Identifying the multifractional function of a Gaussian process. Stat. Probab. Lett.39 (1998) 337–345. Zbl0931.60022MR1646220
  4. [4] N. Chentsov, Lévy’s Brownian motion of several parameters and generalized white noise. Theory Probab. Appl.2 (1957) 265–266. 
  5. [5] J. Faraut and H. Harzallah, Distances hilbertiennes invariantes sur un espace homogène. Ann. Inst. Fourier24 (1974) 171–217. Zbl0265.43013MR365042
  6. [6] A. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertsche Raum (German). C. R. (Dokl.) Acad. Sci. URSS 26 (1940) 115–118. Zbl0022.36001MR3441
  7. [7] C. Lacaux, Real harmonizable multifractional Lévy motions. Ann. Inst. Henri Poincaré40 (2004) 259–277. Zbl1041.60038MR2060453
  8. [8] C. Lacaux, Series representation and simulation of multifractional Lévy motions. Adv. Appl. Probab.36 (2004) 171–197. Zbl1053.60008MR2035779
  9. [9] P. Lévy, Processus stochastiques et mouvement Brownien. Gauthier-Villars (1965). Zbl0034.22603MR190953
  10. [10] J. Istas, Spherical and hyperbolic fractional Brownian motion. Electron. Commun. Probab.10 (2005) 254–262. Zbl1112.60029MR2198600
  11. [11] J. Istas, On fractional stable fields indexed by metric spaces. Electron. Commun. Probab.11 (2006) 242–251. Zbl1110.60032MR2266715
  12. [12] J. Istas and C. Lacaux, On locally self-similar fractional random fields indexed by a manifold. Preprint (2009). Zbl1293.60056MR3176470
  13. [13] B. Mandelbrot and J. Van Ness, Fractional Brownian motions, fractional noises and applications. SIAM Review10 (1968) 422–437. Zbl0179.47801MR242239
  14. [14] R. Peltier and J. Lévy-Vehel, Multifractional Brownian motion : definition and preliminary results. Rapport de recherche de l’INRIA 2645 (1996). 
  15. [15] A. Valette, Les représentations uniformément bornées associées à un arbre réel. Bull. Soc. Math. Belgique42 (1990) 747–760. Zbl0727.43002MR1316222

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