A note on the functional law of the iterated logarithm for Lévy's area process

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Department of Mathematics, University of Abidjan, 22 BP 582 Abidjan 22, Ivory Coast
Department of Mathematics, Cadi Ayyad University, BP S15, Marrakech, Morocco

By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.

law of the iterated logarithm, Lévy's area process, Brownian motion, maximum likelihood

P. Baldi, Large deviations and functional iterated logarithm law for diffusion processes, Probab. Theory Related Fields 71 (1986), 435-453.
P. Baldi, G. Ben Arous and G. Kerkyacharian, Large deviations and Strassen theorem in Hölder norm, Stochastic Process. Appl. 42 (1992), 171-180.
G. Ben Arous and M. Ledoux, Grandes déviations de Freidlin-Wentzell en norme hölderienne, in: Lecture Notes in Math. 1583, Springer, 1994, 293-299.
T. Chan, D. Dean, K. Jansons and L. Rogers, Polymer conformations in elongational flows, Comm. Math. Phys. 160 (1994), 239-257.
K. Helmes, B. Rémillard and R. Theodorescu, The functional law of the iterated logarithm for Lévy's area process, in: Lecture Notes in Control and Inform. Sci. 96, Springer, 1986, 338-345.
K. Helmes and A. Schwane, Lévy's stochastic area formula in higher dimensions, J. Funct. Anal. 54 (1983), 117-192.
N. Ikeda, S. Kusuoka and S. Manabe, Lévy's stochastic area formula for Gaussian processes, Comm. Pure Appl. Math. 4 (1994), 329-360.
P. Lévy, Le mouvement brownien plan, Amer. J. Math. 62 (1940), 487-550.
R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes, Vol. 2, Springer, New York, 1977.
M. , B. Rémillard and R. Theodorescu, Between Strassen and Chung normalizations for Lévy's area process, Statist. Probab. Letters, to appear.
B. Rémillard, On Chung's law of the iterated logarithm for some stochastic integrals, Ann. Probab. 22 (1994), 1794-1802.