Finitary isomorphisms of continuous-time processes
Consider two translation-invariant continuous-time processes $X=(X_t)$ and $Y=(Y_t)$.
The two processes are isomorphic if there exists an invertible (bimeasurable) map from $X$ to $Y$ which commutes with translations.
The map is finitary if in order to determine a portion of $Y$ one only needs to see a large portion of $X$.
When does such a finitary map exist? We investigate this question, showing, for example,
that Brownian motion reflected on an interval is finitarily isomorphic to a Poisson point process (thereby answering a question of Kosloff and Soo).