Abstract
Let Z(t)=(Z1(t),…,Zd(t))⊤,t∈R where Zi(t),t∈R, i=1,…,d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For X(t)=AZ(t),t∈R, where A is a nonsingular d×d real-valued matrix, u,c∈Rd and T>0 we derive tight bounds for P∃t∈[0,T]:∩i=1d{Xi(t)−cit>ui}and find exact asymptotics as (u1,…,ud)⊤=(ua1,…,uad)⊤ for any (a1,…,ad)⊤∈Rd∖(−∞,0]d and u→∞.
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