Schrödinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as $h$-transforms in the sense of Doob for some space-time harmonic function $h$ of Brownian motion, and also as solutions to a large deviation problem introduced by Schrödinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrödinger processes of infinite-dimensional Brownian motion. The results and examples concerning entropy minimization with given marginals are of independent interest.
"Entropy minimization and Schrödinger processes in infinite dimensions." Ann. Probab. 25 (2) 901 - 926, April 1997. https://doi.org/10.1214/aop/1024404423