Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics.

For { B H (t) = (B H , 1 (t) , ... , B H , d (t)) ⊤ , t ≥ 0 } , where { B H , i (t) , t ≥ 0 } , 1 ≤ i ≤ d are mutually independent fractional Brownian motions, we obtain the exact asymptotics of P (∃ t ≥ 0 : A B H (t) - μ t > ν u) , u → ∞ , where A is a non-singular d × d matrix and μ = (μ 1 , ... , μ d) ⊤ ∈ R d , ν = (ν 1 , ... , ν d) ⊤ ∈ R d are such that there exists some 1 ≤ i ≤ d such that μ i > 0 , ν i > 0. [ABSTRACT FROM AUTHOR]