Naslov
A distributional equality for suprema of spectrally positive Levy processes

Autori
Geček Tuđen, Ivana ; Vondraček, Zoran

Izvornik
Journal of theoretical probability (0894-9840) 29 (2016), 3; 826-842

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Spectrally positive Levy process ; subordinator ; supremum ; distributional equality

Sažetak
Let $Y$ be a spectrally positive L\'evy process with $\E Y_1<0$, $C$ an independent subordinator with finite expectation, and $X=Y+C$. A curious distributional equality proved in \cite{; ; ; ; ; ; HPSV04a}; ; ; ; ; ; states that if $\E X_1<0$, then $\sup_{; ; ; ; ; ; 0\le t <\infty}; ; ; ; ; ; Y_t$ and the supremum of $X$ just before the first time its new supremum is reached by a jump of $C$ have the same distribution. In this paper we give an alternative proof of an extension of this result and offer an explanation why it is true.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA