Annales Mathématiques
Blaise Pascal
no. 2
On the local time of sub-fractional Brownian motion
Ibrahima Mendy1
1 Université de Ziguinchor UFR Sciences et Technologies Département de Mathématiques BP 523 Ziguinchor Senegal.
Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 357-374.

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].

DOI : 10.5802/ambp.288
Classification : 60G15, 60G17, 60G18
Mots clés : Sub-fractional Brownian motion, local time, local nondeterminism, Chung’s type law of iterated logarithm

Ibrahima Mendy 1

1 Université de Ziguinchor UFR Sciences et Technologies Département de Mathématiques BP 523 Ziguinchor Senegal. 
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Ibrahima Mendy. On the local time of sub-fractional Brownian motion. Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 357-374. doi : 10.5802/ambp.288. https://ambp.centre-mersenne.org/articles/10.5802/ambp.288/

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