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

Modeste N’zi; M’hamed Eddahbi

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 2, page 223-229
  • ISSN: 1233-7234

Abstract

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

How to cite

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N’zi, Modeste, and Eddahbi, M’hamed. "A note on the functional law of the iterated logarithm for Lévy's area process." Applicationes Mathematicae 24.2 (1997): 223-229. <http://eudml.org/doc/219164>.

@article{N1997,
abstract = {By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.},
author = {N’zi, Modeste, Eddahbi, M’hamed},
journal = {Applicationes Mathematicae},
keywords = {law of the iterated logarithm; Lévy's area process; Brownian motion; maximum likelihood; Lévy's stochastic area process; P-a.s. relatively compact; Hölder topology},
language = {eng},
number = {2},
pages = {223-229},
title = {A note on the functional law of the iterated logarithm for Lévy's area process},
url = {http://eudml.org/doc/219164},
volume = {24},
year = {1997},
}

TY - JOUR
AU - N’zi, Modeste
AU - Eddahbi, M’hamed
TI - A note on the functional law of the iterated logarithm for Lévy's area process
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 2
SP - 223
EP - 229
AB - By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
LA - eng
KW - law of the iterated logarithm; Lévy's area process; Brownian motion; maximum likelihood; Lévy's stochastic area process; P-a.s. relatively compact; Hölder topology
UR - http://eudml.org/doc/219164
ER -

References

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  1. [1] P. Baldi, Large deviations and functional iterated logarithm law for diffusion processes, Probab. Theory Related Fields 71 (1986), 435-453. Zbl0587.60074
  2. [2] P. Baldi, G. Ben Arous and G. Kerkyacharian, Large deviations and Strassen theorem in Hölder norm, Stochastic Process. Appl. 42 (1992), 171-180. Zbl0757.60014
  3. [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. Zbl0811.60019
  4. [4] T. Chan, D. Dean, K. Jansons and L. Rogers, Polymer conformations in elongational flows, Comm. Math. Phys. 160 (1994), 239-257. Zbl0790.60057
  5. [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. Zbl0637.60043
  6. [6] K. Helmes and A. Schwane, Lévy's stochastic area formula in higher dimensions, J. Funct. Anal. 54 (1983), 117-192. Zbl0522.60082
  7. [7] N. Ikeda, S. Kusuoka and S. Manabe, Lévy's stochastic area formula for Gaussian processes, Comm. Pure Appl. Math. 4 (1994), 329-360. Zbl0803.60037
  8. [8] P. Lévy, Le mouvement brownien plan, Amer. J. Math. 62 (1940), 487-550. Zbl66.0619.02
  9. [9] R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes, Vol. 2, Springer, New York, 1977. Zbl0556.60003
  10. [10] M. , B. Rémillard and R. Theodorescu, Between Strassen and Chung normalizations for Lévy's area process, Statist. Probab. Letters, to appear. Zbl0897.60037
  11. [11] B. Rémillard, On Chung's law of the iterated logarithm for some stochastic integrals, Ann. Probab. 22 (1994), 1794-1802. Zbl0840.60030

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