Item description for Stochastic Models of Structural Plasma Turbulence (Modern Probability and Statistics) by V. Korolev & N. Skvortsova...
Five years ago a series of seminars on Stochastic Structures in Plasma Turbulence was initiated by physicists and mathematicians from various academic centers in Russia aimed at the construction of adequate probabilistic models which can explain the departure of the experimental data from the classical theory. This book contains both a selection of most important reviews published in 2003 in the Russian version of the seminar proceedings as well as new papers dealing with recent investigations in plasma physics and financial mathematics.
The collection contains papers presenting various viewpoints on structural plasma turbulence. The collection begins with an article devoted to the research on ionacoustic turbulence in current-carrying magnetized plasma. Other topics treated in this volume are: low-frequency strong structural turbulence in toroidal plasma confinement systems; experimental time samples of particle fluxes in low-frequency strong structural (LF SS) turbulence; diffusion processes in LF SS turbulence; multifractal models of plasma turbulence. One of main topics discussed in the papers of the collection is the heavy-tailedness of the probability distributions of the characteristics of the processes observed in turbulent plasmas. A special paper gives a comprehensive review of the properties of the so-called fractionally stable distributions which appear as limits for continuous-time random walks which are often used for modeling chaotic processes. Much attention is paid to mixtures of normal distributions and hidden Markov models.
A new powerful method is proposed for the statistical analysis of chaotic stochastic processes, the so-called method of moving separation of mixtures. This method was originally designed for the study of the evolution of financial indexes, but proved to be very efficient for the analysis of time series representing data accumulated in experiments with turbulent plasmas. The corresponding theory is developed which proposes a new multidimensional interpretation of volatility of chaotic stochastic processes.
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