  We took advantage of the observations carried out by XMM in the COSMOS field
during 3.5 years, to study the long term variability of a large sample of AGN
(638 sources), in a wide range of redshift (0.1<z<3.5) and X-ray luminosity
($10^{41}<$L(2-10)$<10^{45.5}$). Both a simple statistical method to asses the
significance of variability, and the Normalized Excess Variance
($\sigma^{2}_{rms}$) parameter, where used to obtain a quantitative measurement
of the variability. Variability is found to be prevalent in most AGN, whenever
we have good statistic to measure it, and no significant differences between
type-1 and type-2 AGN were found. A flat (slope -0.23+/-0.03) anti-correlation
between $\sigma^{2}_{rms}$ and X-ray luminosity is found, when significantly
variable sources are considered all together. When divided in three redshift
bins, the anti-correlation becomes stronger and evolving with z, with higher
redshift AGN being more variable. We prove however that this effect is due to
the pre-selection of variable sources: considering all the sources with
available $\sigma^{2}_{rms}$ measurement, the evolution in redshift disappears.
For the first time we were also able to study the long term X-ray variability
as a function of $M_{\rm BH}$ and Eddington ratio, for a large sample of AGN
spanning a wide range of redshift. An anti-correlation between
$\sigma^{2}_{rms}$ and $M_{\rm BH}$ is found, with the same slope of the
anti-correlation between $\sigma^{2}_{rms}$ and X-ray luminosity, suggesting
that the latter can be a byproduct of the former one. No clear correlation is
found between $\sigma^{2}_{rms}$ and the Eddington ratio in our sample.
Finally, no correlation is found between the X-ray $\sigma^{2}_{rms}$ and the
optical variability.
