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Slučajne mere subordinatorskega tipa
出版Inštitut za matematiko, fiziko in mehaniko, 1990
URLhttp://books.google.com.hk/books?id=AzlMNQAACAAJ&hl=&source=gbs_api
註釋A non-decrasing process $(Y_t: 0\le t\le 1)$ with cadlag paths can be viewed as the distribution function of a random measure. Here the research has been focused on random discrete measures arising from subordinators. The distribution function of these measures can be written as $(\frac{\xi_t} {\xi_1}:0\le t\le 1)$ where $(\xi_t:t\ge 0)$ is a process with independent, non-negative, stationary increments that only increase in jumps. Such processes will be referred to as subordinators without drift in the sequel. The purpose of the project was to find the distribution of the largest atom in a random measure arising form a subordinator, or, more generally, the distribution of the first $n$ largest atoms. Another question was to find out when a given random probability measure arises from subordinators. This year the researchers were able to derive integral equations for the density of the distribution of the $n$ largest atoms in a random measure arising from subordinators. Their approach was particularly successful in the Dirichlet case and in the stable case. The question about how to characterise random measures arising from subordinators has not yet been solved completely. A few new necessary conditions have been found, however.