On the ruin probability for physical fractional Brownian motion

摘要

We derive the exact asymptotic behavior of the ruin probability P{X(t) > x for some t > 0} for the process X(t) = integral(0)(1) xi(s) ds - ct, with respect to level x which tends to infinity. We assume that the underlying process xi(t) is a.s. continuous stationary Gaussian with mean zero and correlation function regularly varying at infinity with index -a is an element of (- 1, 0). (C) 2004 Elsevier B.V. All rights reserved.