  This paper derives the asymptotic behavior of $$\mathbb{P} \{
\int\limits_0^\infty \mathbb{I}\Big(B_H(s)-c_1s>q_1u,
B_H(s)-c_2s>q_2u\Big)ds>T_u\},\quad u \to \infty,$$ where $B_H$ is a fractional
Brownian motion, $c_1,c_2,q_1,q_2>0,\ H \in (0,1), \ T_u \ge 0$ is a measurable
function and $\mathbb{I}(\cdot)$ is the indicator function.

Probability