Sojourns of a two-dimensional fractional Bronwian motion risk process


Grigori Jasnovidov




This paper derives the asymptotic behavior of P ∞∫ 0 I ( BH(s) − c1s > q1u,BH(s) − c2s > q2u ) ds > Tu , u →∞, where BH is a fractional Brownian motion, c1, c2, q1, q2 > 0, H ∈ (0, 1), Tu ≥ 0 is a measurable function and I(·) is the indicator function.