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- W4366281009 abstract "In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with $$L^2$$ -Wasserstein metric tensor, via the Wong–Zakai approximation. We begin our investigation by showing that the stochastic Euler–Lagrange equation, regardless it is deduced from either the variational principle or particle dynamics, can be interpreted as the stochastic kinetic Hamiltonian flows in Wasserstein manifold. We further propose a novel variational formulation to derive more general stochastic Wasserstein Hamiltonian flows, and demonstrate that this new formulation is applicable to various systems including the stochastic Schrödinger equation, Schrödinger equation with random dispersion, and Schrödinger bridge problem with common noise." @default.
- W4366281009 created "2023-04-20" @default.
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- W4366281009 date "2023-04-18" @default.
- W4366281009 modified "2023-09-25" @default.
- W4366281009 title "Stochastic Wasserstein Hamiltonian Flows" @default.
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- W4366281009 doi "https://doi.org/10.1007/s10884-023-10264-4" @default.
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