Weak convergence to fractional Brownian motion in some anisotropic Besov space

M. Ait Ouahra[1]

  • [1] Cadi Ayyad University Faculty of Sciences Semlalia Departement of Mathematics B.P. 2390 Marrakech 40000 MOROCCO

Annales mathématiques Blaise Pascal (2004)

  • Volume: 11, Issue: 1, page 1-17
  • ISSN: 1259-1734

Abstract

top
We give some limit theorems for the occupation times of 1-dimensional Brownian motion in some anisotropic Besov space. Our results generalize those obtained by Csaki et al. [4] in continuous functions space.

How to cite

top

Ait Ouahra, M.. "Weak convergence to fractional Brownian motion in some anisotropic Besov space." Annales mathématiques Blaise Pascal 11.1 (2004): 1-17. <http://eudml.org/doc/10496>.

@article{AitOuahra2004,
abstract = {We give some limit theorems for the occupation times of 1-dimensional Brownian motion in some anisotropic Besov space. Our results generalize those obtained by Csaki et al. [4] in continuous functions space.},
affiliation = {Cadi Ayyad University Faculty of Sciences Semlalia Departement of Mathematics B.P. 2390 Marrakech 40000 MOROCCO},
author = {Ait Ouahra, M.},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {1},
number = {1},
pages = {1-17},
publisher = {Annales mathématiques Blaise Pascal},
title = {Weak convergence to fractional Brownian motion in some anisotropic Besov space},
url = {http://eudml.org/doc/10496},
volume = {11},
year = {2004},
}

TY - JOUR
AU - Ait Ouahra, M.
TI - Weak convergence to fractional Brownian motion in some anisotropic Besov space
JO - Annales mathématiques Blaise Pascal
DA - 2004/1//
PB - Annales mathématiques Blaise Pascal
VL - 11
IS - 1
SP - 1
EP - 17
AB - We give some limit theorems for the occupation times of 1-dimensional Brownian motion in some anisotropic Besov space. Our results generalize those obtained by Csaki et al. [4] in continuous functions space.
LA - eng
UR - http://eudml.org/doc/10496
ER -

References

top
  1. J. Bergh, J. Löfström, Interpolation spaces. An introduction, (1976), Springer-Verlag Zbl0344.46071MR482275
  2. P. Billingsley, Convergence of Probability measures, (1968), Wiley, New York Zbl0172.21201MR233396
  3. Z. Ciesielski, G. Keryacharian, B. Roynette, Quelques espaces fonctionels associes à des processus Gaussiens, Studia Math 107 (1993), 171-204 Zbl0809.60004MR1244574
  4. E. Csaki, Z. Shi, M. Yor, Fractional Brownian motions as ”higher-order” fractional derivatives of Brownian local times Zbl1030.60073MR1979974
  5. J. Jacod, A. N. Shiryaev, Limit theorems for stochastic processes, 288 (1987), Springer, Berlin Zbl0635.60021MR959133
  6. A. Kamont, Isomorphism of some anisotropic Besov and sequence spaces, Studia. Math 110 (1994), 169-189 Zbl0810.41010MR1279990
  7. A. Kamont, On the fractional anisotropic Wiener field, Prob. and Math. Statistics 16 (1996), 85-98 Zbl0857.60046MR1407935
  8. A. A. Kilbas, O. I. Marichev, S. G. Samko, Fractional integrals and derivatives. Theory and applications, (1993), Gordon and Breach Science Publishers Zbl0818.26003MR1347689
  9. J. Lamperti, On convergence of stochastic processes, Trans. Amer. Math. Soc 104 (1962), 430-435 Zbl0113.33502MR143245
  10. M. B. Marcus, J. Rosen, p –variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments, Ann. Prob 20 (1992), 1685-1713 Zbl0762.60069MR1188038
  11. H. P. McKean, A Hölder condition for Brownian local time, J. Math. Kyoto Univ 1 (1962), 195-201 Zbl0121.13101MR146902
  12. J. Peetre, New thoughts on Besov spaces, (1976), Duke Univ. Math. Series, Durham, NC Zbl0356.46038MR461123
  13. E. C. Titchmarsh, Introduction to the theory of Fourier integrals, (1948), Second edition. Clarendon Press, Oxford Zbl0017.40404
  14. H. R. Trotter, A property of Brownian motion paths, Illinois. J. Math 2 (1958), 425-433 Zbl0117.35502MR96311
  15. T. Yamada, On the fractional derivative of Brownian local times, J. Math. Kyoto Univ 25 (1985), 49-58 Zbl0625.60090MR777245

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.