Modeling Stock Order Book Dynamics with Marked Hawkes Processes

I introduce a model used to describe the fluctuation of tick-by-tick financial time series. The model, based on market point process, allows to incorporate in a unique process the time between different transactions and their volume. The model was already used for the foreign exchange market, and I try to extend it to the stock market, using data sampling in millisecond. The main motivation for the model is the fact that the "excitation" of the market is different in periods of time with low exchanged volume and high volume exchanged.