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.
@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}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {11}, number = {1}, year = {2004}, 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 TI - Weak convergence to fractional Brownian motion in some anisotropic Besov space JO - Annales Mathématiques Blaise Pascal PY - 2004 DA - 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/ UR - https://www.ams.org/mathscinet-getitem?mr=2077234 UR - https://zbmath.org/?q=an%3A1077.60025 UR - https://doi.org/10.5802/ambp.181 DO - 10.5802/ambp.181 LA - en ID - AMBP_2004__11_1_1_0 ER -
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] Interpolation spaces. An introduction, Springer-Verlag, 1976 | MR: 482275 | Zbl: 0344.46071
[2] Convergence of Probability measures, Wiley, New York, 1968 | MR: 233396 | Zbl: 0172.21201
[3] Quelques espaces fonctionels associes à des processus Gaussiens, Studia Math, Volume 107 (1993) no. 2, pp. 171-204 | MR: 1244574 | Zbl: 0809.60004
[4] Fractional Brownian motions as ”higher-order” fractional derivatives of Brownian local times (Bolyai Society Mathematical Studies, to appear) | MR: 1979974 | Zbl: 1030.60073
[5] Limit theorems for stochastic processes, Grundlehren der Mathematischen Wissenchaften, Volume 288, Springer, Berlin, 1987 | MR: 959133 | Zbl: 0635.60021
[6] Isomorphism of some anisotropic Besov and sequence spaces, Studia. Math, Volume 110 (1994) no. 2, pp. 169-189 | MR: 1279990 | Zbl: 0810.41010
[7] On the fractional anisotropic Wiener field, Prob. and Math. Statistics, Volume 16 (1996) no. 1, pp. 85-98 | MR: 1407935 | Zbl: 0857.60046
[8] Fractional integrals and derivatives. Theory and applications, Gordon and Breach Science Publishers, 1993 | MR: 1347689 | Zbl: 0818.26003
[9] On convergence of stochastic processes, Trans. Amer. Math. Soc, Volume 104 (1962), pp. 430-435 | Article | MR: 143245 | Zbl: 0113.33502
[10] –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 | Article | MR: 1188038 | Zbl: 0762.60069
[11] A Hölder condition for Brownian local time, J. Math. Kyoto Univ, Volume 1 (1962), pp. 195-201 | MR: 146902 | Zbl: 0121.13101
[12] New thoughts on Besov spaces, Duke Univ. Math. Series, Durham, NC, 1976 | MR: 461123 | Zbl: 0356.46038
[13] Introduction to the theory of Fourier integrals, Second edition. Clarendon Press, Oxford, 1948
[14] A property of Brownian motion paths, Illinois. J. Math, Volume 2 (1958), pp. 425-433 | MR: 96311 | Zbl: 0117.35502
[15] On the fractional derivative of Brownian local times, J. Math. Kyoto Univ, Volume 25 (1985) no. 1, pp. 49-58 | MR: 777245 | Zbl: 0625.60090
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