engleski

A distributional equality for suprema of spectrally positive Levy processes

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.

Spectrally positive Levy process ; subordinator ; supremum ; distributional equality

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