Multiplicative Schrödinger problem and the Dirichlet transport

DOI10.1007/s00440-020-00987-6zbMath1466.49042arXiv1807.05649OpenAlexW3043820300MaRDI QIDQ2200506

Ting-Kam Leonard Wong, Soumik Pal

Publication date: 22 September 2020

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05649

zbMATH Keywords

large deviationsDirichlet processoptimal transportSchrödinger problem\(L\)-divergencedisplacment interpolationentropic measureexponentially concave function

Mathematics Subject Classification ID

Large deviations (60F10) Random measures (60G57) Optimal transportation (49Q22) Jump processes on general state spaces (60J76)

Related Items (8)

Random concave functions ⋮ When optimal transport meets information geometry ⋮ Pseudo-Riemannian geometry encodes information geometry in optimal transport ⋮ On the difference between entropic cost and the optimal transport cost ⋮ Conformal mirror descent with logarithmic divergences ⋮ Logarithmic divergences from optimal transport and Rényi geometry ⋮ Entropic turnpike estimates for the kinetic Schrödinger problem ⋮ Projections with logarithmic divergences

Cites Work

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• The geometry of relative arbitrage
• A survey of the Schrödinger problem and some of its connections with optimal transport
• On the rate of convergence in Wasserstein distance of the empirical measure
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage
• From the Schrödinger problem to the Monge-Kantorovich problem
• From large deviations to Wasserstein gradient flows in multiple dimensions
• Optimization of relative arbitrage
• Information geometry and its applications
• Stability of a 4th-order curvature condition arising in optimal transport theory
• A convexity principle for interacting gases
• The geometry of optimal transportation
• Logarithmic divergences from optimal transport and Rényi geometry
• Embedding optimal transports in statistical manifolds
• Exponentially concave functions and a new information geometry
• A parallel between Brownian bridges and gamma bridges
• Monge's problem with a quadratic cost by the zero-noise limit of \(h\)-path processes
• The Kähler geometry of certain optimal transport problems
• Entropic measure and Wasserstein diffusion
• Exponentially concave functions and high dimensional stochastic portfolio theory
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
• Large deviations for Dirichlet processes and Poisson-Dirichlet distribution with two parameters
• Eigenvalues of rank-one updated matrices with some applications
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Polar factorization and monotone rearrangement of vector‐valued functions
• Conditioning as disintegration
• The Variational Formulation of the Fokker--Planck Equation
• Information Geometry in Portfolio Theory
• Wasserstein gradient flows from large deviations of many-particle limits
• Elements of Information Theory
• Large deviations for processes with independent increments

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