Weak convergence to fractional Brownian motion in some anisotropic Besov space
Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 1, pp. 1-17

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.

DOI: 10.5802/ambp.181

M. Ait Ouahra  1

1 Cadi Ayyad University Faculty of Sciences Semlalia Departement of Mathematics B.P. 2390 Marrakech 40000 MOROCCO
M. Ait Ouahra. Weak convergence to fractional Brownian motion in some anisotropic Besov space. Annales mathématiques Blaise Pascal, Volume 11 (2004) no. 1, pp. 1-17. doi: 10.5802/ambp.181
@article{AMBP_2004__11_1_1_0,
     author = {M. Ait Ouahra},
     title = {Weak convergence to fractional {Brownian} motion in some anisotropic {Besov} space},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {1--17},
     year = {2004},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {11},
     number = {1},
     doi = {10.5802/ambp.181},
     mrnumber = {2077234},
     zbl = {1077.60025},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.181/}
}
TY  - JOUR
AU  - M. Ait Ouahra
TI  - Weak convergence to fractional Brownian motion in some anisotropic Besov space
JO  - Annales mathématiques Blaise Pascal
PY  - 2004
SP  - 1
EP  - 17
VL  - 11
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - https://ambp.centre-mersenne.org/articles/10.5802/ambp.181/
DO  - 10.5802/ambp.181
LA  - en
ID  - AMBP_2004__11_1_1_0
ER  - 
%0 Journal Article
%A M. Ait Ouahra
%T Weak convergence to fractional Brownian motion in some anisotropic Besov space
%J Annales mathématiques Blaise Pascal
%D 2004
%P 1-17
%V 11
%N 1
%I Annales mathématiques Blaise Pascal
%U https://ambp.centre-mersenne.org/articles/10.5802/ambp.181/
%R 10.5802/ambp.181
%G en
%F AMBP_2004__11_1_1_0

[1] J. Bergh; J. Löfström Interpolation spaces. An introduction, Springer-Verlag, 1976 | Zbl | MR

[2] P. Billingsley Convergence of Probability measures, Wiley, New York, 1968 | Zbl | MR

[3] Z. Ciesielski; G. Keryacharian; B. Roynette Quelques espaces fonctionels associes à des processus Gaussiens, Studia Math, Volume 107 (1993) no. 2, pp. 171-204 | Zbl | MR

[4] E. Csaki; Z. Shi; M. Yor Fractional Brownian motions as ”higher-order” fractional derivatives of Brownian local times (Bolyai Society Mathematical Studies, to appear) | Zbl | MR

[5] J. Jacod; A. N. Shiryaev Limit theorems for stochastic processes, Grundlehren der Mathematischen Wissenchaften, 288, Springer, Berlin, 1987 | Zbl | MR

[6] A. Kamont Isomorphism of some anisotropic Besov and sequence spaces, Studia. Math, Volume 110 (1994) no. 2, pp. 169-189 | Zbl | MR

[7] A. Kamont On the fractional anisotropic Wiener field, Prob. and Math. Statistics, Volume 16 (1996) no. 1, pp. 85-98 | Zbl | MR

[8] A. A. Kilbas; O. I. Marichev; S. G. Samko Fractional integrals and derivatives. Theory and applications, Gordon and Breach Science Publishers, 1993 | Zbl | MR

[9] J. Lamperti On convergence of stochastic processes, Trans. Amer. Math. Soc, Volume 104 (1962), pp. 430-435 | DOI | Zbl | MR

[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, Volume 20 (1992) no. 4, pp. 1685-1713 | DOI | Zbl | MR

[11] H. P. McKean A Hölder condition for Brownian local time, J. Math. Kyoto Univ, Volume 1 (1962), pp. 195-201 | Zbl | MR

[12] J. Peetre New thoughts on Besov spaces, Duke Univ. Math. Series, Durham, NC, 1976 | Zbl | MR

[13] E. C. Titchmarsh Introduction to the theory of Fourier integrals, Second edition. Clarendon Press, Oxford, 1948

[14] H. R. Trotter A property of Brownian motion paths, Illinois. J. Math, Volume 2 (1958), pp. 425-433 | Zbl | MR

[15] T. Yamada On the fractional derivative of Brownian local times, J. Math. Kyoto Univ, Volume 25 (1985) no. 1, pp. 49-58 | Zbl | MR

Cited by Sources: