caa a22 4500 467892334 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10955-005-8076-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8076-9 Nonergodicity of a Time Series Obeying Lévy Statistics [Elektronische Daten] [Gennady Margolin, Eli Barkai] Time-averaged autocorrelation functions of a dichotomous random process switching between 1 and 0 and governed by wide power law sojourn time distribution are studied. Such a process, called a Lévy walk, describes dynamical behaviors of many physical systems, fluorescence intermittency of semiconductor nanocrystals under continuous laser illumination being one example. When the mean sojourn time diverges the process is non-ergodic. In that case, the time average autocorrelation function is not equal to the ensemble averaged autocorrelation function, instead it remains random even in the limit of long measurement time. Several approximations for the distribution of this random autocorrelation function are obtained for different parameter ranges, and favorably compared to Monte Carlo simulations. Nonergodicity of the power spectrum of the process is briefly discussed, and a nonstationary Wiener-Khintchine theorem, relating the correlation functions and the power spectrum is presented. The considered situation is in full contrast to the usual assumptions of ergodicity and stationarity. Springer Science + Business Media, Inc., 2006 Nonergodicity nationallicence Time series nationallicence Lévy statistics nationallicence Power law nationallicence Correlation function nationallicence Margolin Gennady Department of Chemistry and Biochemistry, Notre Dame University, 46556, Notre Dame, IN aut Barkai Eli Department of Chemistry and Biochemistry, Notre Dame University, 46556, Notre Dame, IN aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/1(2006-01-01), 137-167 0022-4715 122:1<137 2006 122 10955 https://doi.org/10.1007/s10955-005-8076-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8076-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Margolin Gennady Department of Chemistry and Biochemistry, Notre Dame University, 46556, Notre Dame, IN aut NATIONALLICENCE 700 1- Barkai Eli Department of Chemistry and Biochemistry, Notre Dame University, 46556, Notre Dame, IN aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/1(2006-01-01), 137-167 0022-4715 122:1<137 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer