What is "subordination" with respect to stochastic processes? I'm building a model for a panel of counts, $\{n_{kt}\}_{k,t}$.
As I read about regression methods for count models and the stochastic processes behind them, the concept of one random variable being "subordinated" to another often comes up (for example in Kozubowski and Podgorski, 2009). What does this mean? In particular, how does one read notation like $X_U$?

A subordinator is a concept that applies to Lévy processes, where it is used as a stochastic time change which is itself an almost surely increasing Lévy process. 
The thing is that the resulting process is still itself a Lévy process which is why it attracts interest. You can have a look at this paper. In general, every book on Lévy processes and stochastic calculus treats the subject, for example the book by Applebaum must have a section on this.
