Hopf-Cole transformation via generalized Schrödinger bridge problem

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.

References in corpus (2)

• Transport information geometry I: Riemannian calculus on probability simplex
• A discrete Schrodinger equation via optimal transport on graphs

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