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The Brenier-Schr\'odinger problem with respect to Feller semimartingales and non-local Hamilton-Jacobi-Bellman equations
- Publication Year :
- 2024
-
Abstract
- Motivated by a problem from incompressible fluid mechanics of Brenier (JAMS 1989), and its recent entropic relaxation by Arnaudo, Cruizero, L\'eonard & 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.<br />Comment: 13 pages, comments welcome!
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.17305
- Document Type :
- Working Paper