2014/12/15 by Yongxin Chen, Tryphon Georgiou, Tryphon T. Georgiou +4 · 1 voice · 8 citations
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #93E20 #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Systems and Control (eess.SY) #eess.SY #electronic engineering #information engineering #math-ph #math.OC #math.PR
paper · pdf · doi:10.48550/arxiv.1412.4430
openalex publication_date 2014/12/15 · arxiv published 2014/12/15 · arxiv updated 2014/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We take a new look at the relation between the optimal transport problem and the Schrödinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing literature. In particular: a) We give an elementary derivation of the Benamou-Brenier fluid dynamics version of the optimal transport problem; b) We provide a new fluid dynamics version of the Schrödinger bridge problem; c) We observe that the latter provides an important connection with optimal transport without zero noise limits; d) We propose and solve a fluid dynamic version of optimal transport with prior; e) We can then view optimal transport with prior as the zero noise limit of Schrödinger bridges when the prior is any Markovian evolution. In particular, we work out the Gaussian case. A numerical example of the latter convergence involving Brownian particles is also provided.