Local time and related sample paths of filtered white noises

Raby Guerbaz[1]

  • [1] Department of Mathematics Faculty of Sciences Semlalia Cady Ayyad University B.P. 2390 Marrakech MORROCO

Annales mathématiques Blaise Pascal (2007)

  • Volume: 14, Issue: 1, page 77-91
  • ISSN: 1259-1734

Abstract

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We study the existence and the regularity of the local time of filtered white noises X = { X ( t ) , t ∈ [ 0 , 1 ] } . We will also give Chung’s form of the law of iterated logarithm for X , this shows that the result on the Hölder regularity, with respect to time, of the local time is sharp.

How to cite

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Guerbaz, Raby. "Local time and related sample paths of filtered white noises." Annales mathématiques Blaise Pascal 14.1 (2007): 77-91. <http://eudml.org/doc/10542>.

@article{Guerbaz2007,
abstract = {We study the existence and the regularity of the local time of filtered white noises $X=\lbrace X(t),\ t\in [0,1]\rbrace $. We will also give Chung’s form of the law of iterated logarithm for $X$, this shows that the result on the Hölder regularity, with respect to time, of the local time is sharp.},
affiliation = {Department of Mathematics Faculty of Sciences Semlalia Cady Ayyad University B.P. 2390 Marrakech MORROCO},
author = {Guerbaz, Raby},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Local time; Local nondeterminism; Chung’s type law of iterated logarithm; Filtered white noises; Local nondeterminizm; Chung's law of iterated logarithm; Filtered White Noise},
language = {eng},
month = {1},
number = {1},
pages = {77-91},
publisher = {Annales mathématiques Blaise Pascal},
title = {Local time and related sample paths of filtered white noises},
url = {http://eudml.org/doc/10542},
volume = {14},
year = {2007},
}

TY - JOUR
AU - Guerbaz, Raby
TI - Local time and related sample paths of filtered white noises
JO - Annales mathématiques Blaise Pascal
DA - 2007/1//
PB - Annales mathématiques Blaise Pascal
VL - 14
IS - 1
SP - 77
EP - 91
AB - We study the existence and the regularity of the local time of filtered white noises $X=\lbrace X(t),\ t\in [0,1]\rbrace $. We will also give Chung’s form of the law of iterated logarithm for $X$, this shows that the result on the Hölder regularity, with respect to time, of the local time is sharp.
LA - eng
KW - Local time; Local nondeterminism; Chung’s type law of iterated logarithm; Filtered white noises; Local nondeterminizm; Chung's law of iterated logarithm; Filtered White Noise
UR - http://eudml.org/doc/10542
ER -

References

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  9. D. Geman, J. Horowitz, Occupation densities, Ann. of Probab. 8 (1980), 1-67 Zbl0499.60081MR556414
  10. W. Li, Q. M. Shao, Gaussian Processes : Inequalities, Small Ball Probabilities and Applications, Stochastic Processes: Theory and methods. Handbook of Statistics 19 (2001), 533-598, UhlenbeckK.K. Zbl0987.60053MR1861734
  11. D. Monrad, H. Rootzén, Small values of Gaussian processes and functional laws of the iterated logarithm, Probab. Th. Rel. Fields 101 (1995), 173-192 Zbl0821.60043MR1318191
  12. L.D. Pitt, Local times for Gaussian vector fields, Indiana Univ. Math. J. 27 (1978), 309-330 Zbl0382.60055MR471055
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  14. Y. Xiao, Strong local nondeterminism and the sample path properties of Gaussian random fields, (2005) 

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