An inductively defined system of Schrodinger problems -- variational problems minimizing relative entropy over probability measures with prescribed endpoint marginals -- together with the coupled functional (Euler) equations that characterize their minimizers. Students learn how existence and uniqueness of solutions to this system yield a stochastic optimal-transport analogue of the Knothe-Rosenblatt rearrangement, extending the classical single Schrodinger problem to a multi-marginal, coordinate-wise construction.
The authors propose and study a system of Schrodinger's problems and functional equations in probability theory. Each Schrodinger problem is a variational problem minimizing relative entropy over pro…