Comparison of two components of a bivariate subordinator and study of the upper envelope of a Lévy process (Q1413101)

For a bivariate subordinator \((Y,Z)\) sufficient conditions for \(\lim(Y_t/Z_t)\to 0\) if \(t\to 0\) or \(\infty\) are obtained. For a Lévy process \(X\) and a subadditive function \(f\) necessary and sufficient conditions are presented for \[ \varliminf\;{\sup\{X_s, s\leq t\}\over f(t)}=\quad \begin{cases} 0, & t\to 0\\ \infty, & t\to \infty.\end{cases} \] {}.