On the local time of sub-fractional Brownian motion

Ibrahima Mendy[1]

  • [1] Université de Ziguinchor UFR Sciences et Technologies Département de Mathématiques BP 523 Ziguinchor Senegal.

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 2, page 357-374
  • ISSN: 1259-1734

Abstract

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S H = { S t H , t ≥ 0 } be a sub-fractional Brownian motion with H ∈ ( 0 , 1 ) . We establish the existence, the joint continuity and the Hölder regularity of the local time L H of S H . We will also give Chung’s form of the law of iterated logarithm for S H . This results are obtained with the decomposition of the sub-fractional Brownian motion into the sum of fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. This decomposition is given by Ruiz de Chavez and Tudor [10].

How to cite

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Mendy, Ibrahima. "On the local time of sub-fractional Brownian motion." Annales mathématiques Blaise Pascal 17.2 (2010): 357-374. <http://eudml.org/doc/116357>.

@article{Mendy2010,
abstract = {$S^\{H\}=\lbrace S^\{H\}_\{t\}, t\ge 0\rbrace $ be a sub-fractional Brownian motion with $H\in (0,1)$. We establish the existence, the joint continuity and the Hölder regularity of the local time $L^\{H\}$ of $S^\{H\}$. We will also give Chung’s form of the law of iterated logarithm for $S^\{H\}$. This results are obtained with the decomposition of the sub-fractional Brownian motion into the sum of fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. This decomposition is given by Ruiz de Chavez and Tudor [10].},
affiliation = {Université de Ziguinchor UFR Sciences et Technologies Département de Mathématiques BP 523 Ziguinchor Senegal.},
author = {Mendy, Ibrahima},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Sub-fractional Brownian motion; local time; local nondeterminism; Chung’s type law of iterated logarithm; sub-fractional Brownian motion; Chung's type law of iterated logarithm},
language = {eng},
month = {7},
number = {2},
pages = {357-374},
publisher = {Annales mathématiques Blaise Pascal},
title = {On the local time of sub-fractional Brownian motion},
url = {http://eudml.org/doc/116357},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Mendy, Ibrahima
TI - On the local time of sub-fractional Brownian motion
JO - Annales mathématiques Blaise Pascal
DA - 2010/7//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 2
SP - 357
EP - 374
AB - $S^{H}=\lbrace S^{H}_{t}, t\ge 0\rbrace $ be a sub-fractional Brownian motion with $H\in (0,1)$. We establish the existence, the joint continuity and the Hölder regularity of the local time $L^{H}$ of $S^{H}$. We will also give Chung’s form of the law of iterated logarithm for $S^{H}$. This results are obtained with the decomposition of the sub-fractional Brownian motion into the sum of fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. This decomposition is given by Ruiz de Chavez and Tudor [10].
LA - eng
KW - Sub-fractional Brownian motion; local time; local nondeterminism; Chung’s type law of iterated logarithm; sub-fractional Brownian motion; Chung's type law of iterated logarithm
UR - http://eudml.org/doc/116357
ER -

References

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