Abstract
We present a general modeling of the order book, and derive some mathematical results in the zero-intelligence case of Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, using a classical FCLT, that the rescaled-centered price process converges to a Brownian motion.These results were first presented by one of the authors (A. J.) at the Market Microstructure: confronting many viewpoints conference in Paris on December 6th, 2010, and at the QMF conference in Sydney on December 17th, 2010.
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