Long Range Dependence, Heavy Tails and Communication Networks

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This project is centered on connections between long range dependence and heavy tails. The primary application areas are data networks, finance, actuarial research and industrial engineering. The project includes a consideration of statistical issues related to detection of long range dependence, self-similarity and multifractality as well as fundamental issues of basic concepts being inadequately defined. For instance, long range dependence is often defined in terms of correlations but these may be either undefined due to the presence of heavy tails or for non-Gaussian processes rather uninformative. Our society is a fast moving and changing one, with ever increasing amounts of information being moved from one end of the country to the other. Dramatic technological and scientific advances are, often, day-to-day phenomena. The stock market is very volatile. The Internet and other communication networks are susceptible to overloads and delays and because of their crucial role in our economic and public life, one needs to be concerned with their performance. Appropriate models are required to make sense of these wildly oscillating processes. This project is centered on models appropriate to understanding and controlling these phenomena-- models with heavy tails and/or long range dependence.