UBC Probability Seminar: Yinon Spinka

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).