Comparison of two components of a bivariate subordinator and study of the upper envelope of a Lévy process. (Comparaison des deux composantes d’un subordinateur bivarié, puis étude de l’enveloppe supérieure d’un processus de Lévy.) (French) Zbl 1032.60045

Vigon, Vincent

Ann. Inst. Henri Poincaré, Probab. Stat. 39, No. 6, 993-1011 (2003).

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 \[ \varliminf\;{\sup\{X_s, s\leq t\}\over f(t)}=\quad \begin{cases} 0, & t\to 0\\ \infty, & t\to \infty.\end{cases} \] .

Reviewer: Nijole Kalinauskaitė (Vilnius)

MSC:

60G51	Processes with independent increments; Lévy processes
60G17	Sample path properties

Keywords:

Lévy processes; sample path properties