An application of martingales in the limit to a problem in information science

Abstract

Martingales in the limit (mils) were introduced about two decades ago as nontrivial extensions of martingales. It was proved in 1976 that they have good convergence properties (at least) for real-valued stochastic processes. But, so far there have not been found any “real-life” applications of mils. In this article, we apply the full generality of mils to a problem in information science. There we study the evolution in time of source journals as, e.g., defined by the Institute for Scientific Information (ISI) who selects, on a yearly basis, the most “visible” journals in the world. In this connection one also encounters quasi-martingales.