On the one-sided exit problem for fractional Brownian motion

Details On the one-sided exit problem for fractional Brownian motion On the one-sided exit problem for fractional Brownian motion

2011-01-26

arxiv.org/abs/1101.5072v1

Mathematics

Probability

16p

Scientific paper

We consider the one-sided exit problem for fractional Brownian motion (FBM),
which is equivalent to the question of the distribution of the lower tail of
the maximum of FBM on the unit interval. We improve the bounds given by Molchan
(1999) and shed some light on the relation to the quantity $I$ studied there.

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