Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion

Details Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion

2007-02-12

arxiv.org/abs/math/0702330v1

Mathematics

Probability

20 pages, submitted to Journal of Theoretical Probability

Scientific paper

We give a result of stability in law of the local time of the fractional
Brownian motion with respect to small perturbations of the Hurst parameter.
Concretely, we prove that the law (in the space of continuous functions) of the
local time of the fractional Brownian motion with Hurst parameter $H$ converges
weakly to that of the local time of $B^{H_0}$, when $H$ tends to $H_0$.

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