Hopf-Cole transformation via generalized Schrödinger bridge problem

2019/01/25 by Léger, Flavien, Li, Wuchen · 1 citation
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1901.09051

Abstract

We study generalized Hopf-Cole transformations motivated by the Schrödinger bridge problem, which can be seen as a boundary value Hamiltonian system on the Wasserstein space. We prove that generalized Hopf-Cole transformations are symplectic submersions in the Wasserstein symplectic geometry. Many examples, including a Hopf-Cole transformation for the shallow water equations, are given. Based on this transformation, energy splitting inequalities are provided.

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• Contact Wasserstein Geodesics for Non-Conservative Schrödinger Bridges

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