Records statistics beyond the standard model - Theory and applications

In recent years, there was a surge of interest in the statistics of record-breaking events, not only from scientists, but also from the general public. In sports and in climatology, but also in nature and in economy, observers are interested in the setting and breaking of new records. This cumulative dissertation is dedicated to the study of record-breaking events. It concludes a series of published and hitherto unpublished articles on theory and applications of record statistics. This work mainly consists of five parts. The first part is about the statistics of records in uncorrelated random variables sampled from time-dependent distributions. In particular, we present a simple model of random variables with a linearly growing mean value and discuss its record statistics thoroughly. Furthermore, the effects of rounding on the occurrence of records in series of independent and identically distributed random variables are considered. Then, in part two, these results are applied to explain and model record temperatures in the context of climatic change. Using our minimal model of random variables with a linear drift, we show that global warming has in fact a significant effect on the occurrence and the values of heat and cold records. The third part focuses on records in correlated processes, in particular random walks. A number of different random walk processes are presented and analyzed. We find that their record statistics are surprisingly interesting and manifold. The results derived in this part are important to understand the occurrence of records in financial data, which will be discussed in the fourth part. There it is demonstrated that random walks are helpful to model records in stock data, nevertheless we find significant deviations from the analytical results and propose an alternative model, which describes the stock data more accurately. The final, fifth part is a general review of the recent developments in the study of record-breaking events in time series of time-dependent and correlated random variables