Year: 2025
Type: preprint
Abstract: Jacobi structures are known to generalize Poisson structures, encompassing symplectic, cosymplectic, and Lie-Poisson manifolds. Notably, other intriguing geometric structures -- such as contact and locally conformal symplectic manifolds -- also admit Jacobi structures but do not belong to the Poisson category. In this paper, we employ global stochastic analysis techniques, initially developed by Meyer and Schwartz, to rigorously introduce stochastic Hamiltonian systems on Jacobi manifolds. We then propose a stochastic Hamilton-Jacobi-Bellman (HJB) framework as an alternative perspective on the underlying dynamics. We emphasize that many of our results extend the work of Bismut [Bis80, Bis81] and Lázaro-Camí \& Ortega [LCO08, LCO09]. Furthermore, aspects of our geometric Hamilton-Jacobi theory in the stochastic setting draw inspiration from the deterministic contributions of Abraham \& Marsden [AM78], de León \& Sardón [dLS17], Esen et al. [EdLSZ21], and related literature.
Source: arXiv (Cornell University)
Authors: Wei, Pingyuan, Huang, Qiao, Duan, Jinqiao
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417283181
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