Sample path properties of the local time of multifractional Brownian motion

Details Sample path properties of the local time of multifractional Brownian motion Sample path properties of the local time of multifractional Brownian motion

2007-09-05

arxiv.org/abs/0709.0637v1

Bernoulli 2007, Vol. 13, No. 3, 849-867

Mathematics

Probability

Published at http://dx.doi.org/10.3150/07-BEJ6140 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6140

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^H=(B^{H(t)}(t),t\in\mathbb{R}^+)$. An analogue of Chung's law of the iterated logarithm is studied for $B^H$ and used to obtain the pointwise H\"{o}lder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^H$.

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