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Title: On distribution of order books Authors:  Martin Smid - Institute of Information Theory and Automation (Czech Republic) [presenting]
Abstract: Order-books of limit order markets follow a complicated dynamics with an infinite dimensional state space. Thus, even under simplifying assumptions, their distribution is not analytically tractable. However, the distribution can be described in two steps: a formula for a conditional distribution of order books given the history of trade and quote data exist while the distribution of the trade and quote process may be described recursively. Using these expressions and ergodicity of the process, which is guaranteed under reasonable conditions, parameters of the model may be estimated by maximum likelihood, which is demonstrated on data from several US stock markets.