On the local time of sub-fractional Brownian motion
Annales Mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 357-374.

${S}^{H}=\left\{{S}_{t}^{H},t\ge 0\right\}$ be a sub-fractional Brownian motion with $H\in \left(0,1\right)$. 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 : https://doi.org/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
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Mendy, Ibrahima. 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. http://www.numdam.org/articles/10.5802/ambp.288/

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