Neighbour-dependent point shifts and random exchange models: invariance and attractors

Autor: Muratov, Anton, Zuyev, Sergei
Rok vydání: 2013
Předmět:
Druh dokumentu: Working Paper
Popis: Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint distribution $F$ and which division distributions $G$, the division points is again a renewal process with the same $F$? An evident case is that of degenerate $F$ and $G$. Interestingly, the only other possibility is when $F$ is Gamma and $G$ is Beta with related parameters. In particular, the division points of a Poisson process is again Poisson, if the division distribution is Beta: B$(r,1-r)$ for some $0Comment: 16 pages
Databáze: arXiv