The stochastic nature of gene expression has been widely demonstrated over the last decade. Initially seen as a "noise" with which cells had to cope with, its biological relevance is now an subject of open debate (Kaern et al., Nat. Rev. Genet. 2005 ; Cai et al., Nature 2006 ; Neildez-Nguyen et al., Differentiation 2007). The understanding of the molecular bases of this stochasticity constitute a new field of investigation. It motivates both wet experiments aiming at describing the characteristics of this stochasticity, and theoretical modeling studies aiming at proposing hypothesis for its causes. It is generally admitted that the most important sources of stochasticity reside in the transcription process (Chubb et al., Curr. Biol. 2006 ; Raj et al., PLoS Biol. 2006) that, at least in higher eukaryotes, proceeds through transcriptional bursts. Usually admitted causes of stochasticity are based upon the presence of some transcription factors (TFs) in only very rare copies in the cell. For instance, if a TF is close to its binding site it will induce repeated transcription-initiating events until it gets away, and therefore the way it diffuses (in 3D or in 1D) will have an impact on the resulting stochastic properties. Also, a wide class of models analyse the stochasticity of a gene taking into account the (potentially stochastic) variations over time of the concentration of its TFs. For instance, it has been shown that auto-inhibition reduces stochasticity. But the fact that, even in high and constant concentrations, TFs bind and unbind stochastically is usually not taken into account. Therefore we build a mathematical model for investigating the stochastic properties of the transcription process for an arbitrary number of TFs, assuming high and constant concentrations, and considering cooperation and competition among binding and unbinding. Parameters are TFs concentration, TFs association and dissociation constant for each combination of the other TFs on the promoter, and transcription rate for each combination of TFs on the promoter. Modeling the system as a simple Markov chain, we are able to predict the resulting stochastic properties of the transcription process in terms of power spectrum. This indicator includes the classical coefficient of variation (variance over square mean) used by many authors, but describes the stochastic properties in a much more precise and dynamic fashion (van Zon et al., Biophys. J. 2006 ; Warren et al., J. Chem. Phys. 2006). One additional advantage is that this formalism can be used to compare model predictions to measures on real cells. Simple examples of input parameters demonstrate complex behaviors that can have a high impact on the overall transcription stochasticity. Therefore, this model reveals another potential source of stochasticity the importance of which needs to be tested through wet experiments.