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1996-1997 | 24 | 2 | 223-229

Tytuł artykułu

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

Treść / Zawartość

Języki publikacji

EN

Abstrakty

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

Rocznik

Tom

24

Numer

2

Strony

223-229

Daty

wydano
1997
otrzymano
1996-01-04

Twórcy

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

Bibliografia

  • [1] P. Baldi, Large deviations and functional iterated logarithm law for diffusion processes, Probab. Theory Related Fields 71 (1986), 435-453.
  • [2] P. Baldi, G. Ben Arous and G. Kerkyacharian, Large deviations and Strassen theorem in Hölder norm, Stochastic Process. Appl. 42 (1992), 171-180.
  • [3] G. Ben Arous and M. Ledoux, Grandes déviations de Freidlin-Wentzell en norme hölderienne, in: Lecture Notes in Math. 1583, Springer, 1994, 293-299.
  • [4] T. Chan, D. Dean, K. Jansons and L. Rogers, Polymer conformations in elongational flows, Comm. Math. Phys. 160 (1994), 239-257.
  • [5] 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.
  • [6] K. Helmes and A. Schwane, Lévy's stochastic area formula in higher dimensions, J. Funct. Anal. 54 (1983), 117-192.
  • [7] N. Ikeda, S. Kusuoka and S. Manabe, Lévy's stochastic area formula for Gaussian processes, Comm. Pure Appl. Math. 4 (1994), 329-360.
  • [8] P. Lévy, Le mouvement brownien plan, Amer. J. Math. 62 (1940), 487-550.
  • [9] R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes, Vol. 2, Springer, New York, 1977.
  • [10] M. , B. Rémillard and R. Theodorescu, Between Strassen and Chung normalizations for Lévy's area process, Statist. Probab. Letters, to appear.
  • [11] B. Rémillard, On Chung's law of the iterated logarithm for some stochastic integrals, Ann. Probab. 22 (1994), 1794-1802.

Identyfikator YADDA

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