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http://hdl.handle.net/10397/98875
Title: | Wasserstein Hamiltonian flow with common noise on graph | Authors: | Cui, J Liu, S Zhou, H |
Issue Date: | Apr-2023 | Source: | SIAM journal on applied mathematics, Apr. 2023, v. 83, no. 2, p.484-509 | Abstract: | We study the Wasserstein Hamiltonian flow with a common noise on the density manifold of a finite graph. Under the framework of the stochastic variational principle, we first develop the formulation of stochastic Wasserstein Hamiltonian flow and show the local existence of a unique solution. We also establish a sufficient condition for the global existence of the solution. Consequently, we obtain the global well-posedness for the nonlinear Schrödinger equations with common noise on a graph. In addition, using Wong–Zakai approximation of common noise, we prove the existence of the minimizer for an optimal control problem with common noise. We show that its minimizer satisfies the stochastic Wasserstein Hamiltonian flow on a graph as well. | Keywords: | Stochastic Hamiltonian flow on graph Density manifold Wong–Zakai approximation Optimal transport |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on applied mathematics | ISSN: | 0036-1399 | EISSN: | 1095-712X | DOI: | 10.1137/22M1490697 | Rights: | © 2023 Society for Industrial and Applied Mathematics The following publication Cui, J., Liu, S., & Zhou, H. (2023). Wasserstein Hamiltonian flow with common noise on graph. SIAM Journal on Applied Mathematics, 83(2), 484-509 is available at https://doi.org/10.1137/22M1490697. |
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