Worked with Hawkes Processes and Poisson Point Processes in the past, have been thinking along a Beta distribution however to capture second order statistics so as to have an estimator on conditional variance. From what I’ve read the difficulty adjustment is modeled after simple hysteresis and does its job well.
I’ve found it useful to see the demand and supply side of a given resource as distributions of utility rather than a single point estimator. Not only does this make more sense, but it allows for iterative market-clearing price formation.
A reference on some of the information economics:
Grossman and Stiglitz - On the Impossibility of Informationally Efficient Markets (slides)
I have taken a very market-driven view of turnover within the space.