### The Brenier-Schrödinger with respect to Feller semimartingales and non-local Hamilton-Jacobi-Bellman equations

With B. Huguet. .

Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, Léonard & Zambrini (AIHP PS 2020), we study a problem of entropic minimization on the path space when the reference measure is a generic Feller semimartingale. We show that, under some regularity condition, our problem connects naturally with a, possibly non-local, version of the Hamilton-Jacobi-Bellman equation. Additionally, we study existence of minimizers when the reference measure in a Ornstein-Uhlenbeck process.