On the local time of sub-fractional Brownian motion

Mendy, Ibrahima

Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 357-374.

$S^H=\{S_t^H,t\ge 0\}$ 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].

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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