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- W4313432661 abstract "This paper summarises a new framework of Stochastic Geometric Mechanics that attributes a fundamental role to Hamilton–Jacobi–Bellman (HJB) equations. These are associated with geometric versions of probabilistic Lagrangian and Hamiltonian mechanics. Our method uses tools of the “second-order differential geometry”, due to L. Schwartz and P.-A. Meyer, which may be interpreted as a probabilistic counterpart of the canonical quantization procedure for geometric structures of classical mechanics. The inspiration for our results comes from what is called “Schrödinger’s problem” in Stochastic Optimal Transport theory, as well as from the hydrodynamical interpretation of quantum mechanics. Our general framework, however, should also be relevant in Machine Learning and other fields where HJB equations play a key role." @default.
- W4313432661 created "2023-01-06" @default.
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- W4313432661 date "2022-12-16" @default.
- W4313432661 modified "2023-09-27" @default.
- W4313432661 title "Hamilton–Jacobi–Bellman Equations in Stochastic Geometric Mechanics" @default.
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- W4313432661 doi "https://doi.org/10.3390/psf2022005037" @default.
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