am trying to simulate the SFGK model from the paper "Statistical theory of the Continuous Double Auction", Eric Smith, J. Doyne Farmer, Laszlo Gillemot and Supriya Krishnamurthy .
The model simulates the Limit order book for various parameter values. The arrival processes are assumed to be poisson. The simulations are carried out for a limiting value of the tick size which is zero. However, zero tick size would mean the entire real line. I am uncertain as to how one simulates poisson processes for the entire line. That is essentially the issue. If we do chose a finite set of values with the tick size being non-zero. Then how are the different tick sizes different? They really can be scaled version of unit tick size. I am trying to get information on how to go from finite tick sizes to the zero tick size limit.