On the joint distribution of ladder variables of random walk
The ladder time \(N\) and ladder height \(H\) of a random walk \(\{S_ n, n \geq 1\}\) as a pair \((N,H)\) lie in the domain of attraction of a bivariate stable law if \(S_ 1\) is in a domain of attraction, as was shown by \textit{P. E. Greenwood}, \textit{E. Omey} and \textit{J. L. Teugels} [Z. Wahrscheinlichkeitstheorie Verw. Geb. 61, 527-539 (1982; Zbl 0493.60072)]. We prove a converse. If \(P(S_ n>0)\) converges and \((N,H)\) lies in a bivariate domain of attraction, then \(S_ 1\) is also in a domain of attraction.
domain of attraction of a bivariate stable law
scientific article; zbMATH DE number 569060
scientific article