Log-stable probability density functions, non-stationarity evaluation, and multi-feature autocorrelation analysis of the $\gamma$-ray light curves of blazars.

In this work, we study the probability density functions that best describe the $\gamma$-ray flux distribution of decade-long light curves of a sample of blazars. For averaged behavior over this period, there was maximum likelihood estimated log-stable distribution; for most sources leading to standard log-normal distribution ($\alpha=2$); however, other sources clearly displayed heavy tail distributions ($\alpha<2$), suggesting underlying multiplicative process of infinite variance. For sequences normalized using the found log-stable distributions, there was performed proposed novel non-stationarity and autocorrelation analysis. The former allowed to quantitatively evaluate non-stationarity of each source as maximizing log-likelihood rate of forgetting in modeled evolution of PDFs, also for evaluation of local variability allowing e.g. for anomaly detection suggesting changes of behavior. Discussed autocorrelation analysis looked at lag $l$ dependence of statistical behavior of all $\{(y_t,y_{t+l})\}$ points, described by various mixed moments - allowing to quantitatively point multiple characteristic time scales of the objects, for example, suggesting hidden periodic processes, with statistical interpretations of their contributions.