We formulate a general model of the continuous double auction, covering the models of Maslov [2000], Luckock [2003], Smith at al. [2003] and (partially) the the model of Mike et. al. [2008]. We analytically describe the distribution of the best quotes and the (conditional) distribution of the order books. Based on these  results, we suggest a technique of a statistical inference of the order books and a procedure allowing a Monte Carlo simulation of the modes, much more efficient then a crude simulation. Finally, we study the tails of the price increments: we find them generally fat-tailed but thin-tailed if the initial order book is large enough.

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