We analyze photon statistics of blinking CdSe-ZnS nano-crystals interacting with a continuous wave laser field, showing that the process is described by a ballistic Levy walk. In particular we show that Mandel's Q parameter, describing the fluctuations of the photon counts, increases with time even in the limit of long times. This behavior is in agreement with the theory of Silbey and coworkers [Jung et al. Chemical Physics 284 181 (2002)], and in contrast to all existing examples where Q approaches a constant, independent of time in the long time limit. We then analyze the distribution of the time averaged intensities, showing that they exhibit a non-ergodic behavior, namely the time averages remain random even in the limit of a long measurement time. In particular, the distribution of occupation times in the on state compares favorably to a theory of weak ergodicity breaking of blinking nano-crystals. We show how our data analysis yields information on the amplitudes of power law decaying on and off times distributions, information not available using standard data analysis of on and off times histograms. Photon statistics reveals fluctuations in the intensity of the bright state indicating that it is composed of several states.