Annales Mathématiques
Blaise Pascal
no. 1
Weak convergence to fractional Brownian motion in some anisotropic Besov space
M. Ait Ouahra1
1 Cadi Ayyad University Faculty of Sciences Semlalia Departement of Mathematics B.P. 2390 Marrakech 40000 MOROCCO
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 
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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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.181/

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

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

[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 | MR | Zbl

[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) | MR | Zbl

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

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

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

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

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

[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 | MR | Zbl

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

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

[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 | MR | Zbl

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

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