  We propose a class of stochastic models for a dynamics of limit order book
with different type of liquidities. Within this class of models we study the
one where a spread decreases uniformly, belonging to the class of processes
known as a population processes with uniform catastrophes. The law of large
numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved
for our model with uniform catastrophes. Our results allow us to satisfactorily
explain the volatility and local trends in the prices, relevant empirical
characteristics that are observed in this type of markets. Furthermore, it
shows us how these local trends and volatility are determined by the typical
values of the bid-ask spread. In addition, we use our model to show how large
deviations occur in the spread and prices, such as those observed in flash
crashes.
