US equity markets exhibits similar features[@micciche]. Other variables with mean-reversion, such as volume of transactions (number of trades) present akin distributions. Power-law tails out of the Lévy range have been reported for the PDFs of normalized NYSE stock volumes[@volumes]. More recently, studies of normalized volumes, performed over high resolution data (1-3 minutes) of NYSE and NASDAQ[@vol1] (see also [@vol2]), display PDFs with power-law behavior both at large and small values. We will show that the class of multiplicative processes considered in Sect. \[Sec:mean\_rev\], although general enough, is not able to reproduce, for any value of its parameters, these empirical PDFs in the whole range.

In a realistic model, we must deal with various sources of fluctuations acting upon the collective variable. Then, we propose to include a component that is lacking to suitably model many real processes, that is the presence of fluctuations that act additively, besides the multiplicative noise already taken into account. The latter originates from the internal correlated behavior of the market, representing a sort of endogenous feed-back effect, while additive noise concerns fluctuations of purely external origin or random speculative trading. Then, in Sect. \[Sec:add\_mult\], we present a further generalization that consists in incorporating an independent 