Abstract
We obtain some maximal inequalities for a centered fractional Brownian motion B H , H ∈ (1/2, 1). For a fractional Brownian motion B H with H ∈ (1/2, 1) with a polynomial drift g(·), we study the asymptotic behaviour of the tail distribution function as T → ∞ for fixed a and as a → ∞ for fixed T.
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