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Would someone be able to give me an idea what type of fluid dynamics I could look at for modelling the order book? My background is more signals-related maths (correlation, covariance, fourier etc).

I am interested in modelling the order book based upon the buy/sell pressure within the order book depth.

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I've never heard of using fluid dynamics used to model the order book. Did you see this mentioned some place? – chrisaycock Jul 14 '13 at 20:21
    
a good start is the Markovian jump-diffusion process and that's only for the limit order book ;) – pyCthon Jul 17 '13 at 2:51

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