%0 Book Section %1 statphys23_1084 %A Manzini, M. %A Scalas, E. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K analysis function mittag-leffler power random renewal signal spectrum statphys23 telegraph theory topic-3 %T Mittag-Leffler time-spaced random telegraph signal %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1084 %X We discuss the power spectrum of a random telegraph signal where waiting times are distributed according to the Mittag-Leffler function. The Mittag-Leffler function is a generalization of the exponential distribution that interpolates between a stretched exponential at low waiting times and a power law at high waiting-times. The Mittag-Leffler distribution is defined as follows in terms of its complementary cumulative distribution function (also called survival function): $$ E_\beta (-t^\beta) = \sum_n=0^ınfty (-t^\beta)^n\Gamma (n+1), $$ where $0 < 1$. For $=1$, the (one-parameter) Mittag-Leffler function coincides with the exponential survival function. The first moment of the Mittag-Leffler distribution is already infinite.

@incollection{statphys23_1084, abstract = {We discuss the power spectrum of a random telegraph signal where waiting times are distributed according to the Mittag-Leffler function. The Mittag-Leffler function is a generalization of the exponential distribution that interpolates between a stretched exponential at low waiting times and a power law at high waiting-times. The Mittag-Leffler distribution is defined as follows in terms of its complementary cumulative distribution function (also called survival function): $$ E_{\beta} (-t^{\beta}) = \sum_{n=0}^{\infty} \frac{(-t^{\beta})^n}{\Gamma (\beta n+1)}, $$ where $0 < \beta \leq 1$. For $\beta =1$, the (one-parameter) Mittag-Leffler function coincides with the exponential survival function. The first moment of the Mittag-Leffler distribution is already infinite.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Manzini, M. and Scalas, E.}, biburl = {https://www.bibsonomy.org/bibtex/2e0bb75631ffe99d7f57d403cac3bf2ab/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {6e35265b7469b1c8b03c64e33b7cf8e6}, intrahash = {e0bb75631ffe99d7f57d403cac3bf2ab}, keywords = {analysis function mittag-leffler power random renewal signal spectrum statphys23 telegraph theory topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:38.000+0200}, title = {Mittag-Leffler time-spaced random telegraph signal}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1084}, year = 2007 }