Stable Non-Gaussian Self-Similar Processes with Stationary Increments

Vladas Pipiras is Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. His main research interests focus on stochastic processes exhibiting long-range dependence, self-similarity and other scaling phenomena, as well as on stable, extreme-value and other distributions possessing heavy tails. His other current interests include high-dimensional time series, sampling issues for "big data" and stochastic dynamical systems, with applications in Econometrics, Neuroscience, Engineering, Computer Science and other areas. Vladas Pipiras has written over 50 research papers, and is a coauthor of a graduate textbook on measure theory and probability. Murad S. Taqqu's research involves self-similar processes, their connection to time series with long-range dependence , the development of statistical tests, and the study of non-Gaussian processes whose marginal distributions have heavy tails. He has written more than 250 scientific papers and is the coauthor of a standard reference on stable non-Gaussian random processes. Professor Taqqu is a Fellow of the Institute of Mathematical Statistics and has been elected Member of the International Statistical Institute. He has received a number of awards, including a John Simon Guggenheim Fellowship, the 1995 William J. Bennett Award, the 1996 IEEE W.R.G. Baker Prize, the 2002 EURASIO Best Paper Award and the 2006 ACM/SIGCOMM Test of Time Award.

Preliminaries.- Minimality, Rigidity, and Flows.- Mixed Moving Averages and Self-similarity.- A. Historical Notes.- B. Standard Lebesgue Spaces and Projections.- C. Notation Summary.