Global Tensor Field Formulation of the Fokker-Planck Equation on Riemannian Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915873962328064 |
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| author | Lee, Taeyoung Chirikjian, Gregory S. |
| author_facet | Lee, Taeyoung Chirikjian, Gregory S. |
| contents | This paper presents a global, coordinate-free formulation of the Fokker-Planck equation on Riemannian manifolds. In the Stratonovich formulation, the infinitesimal generator is expressed intrinsically through Lie derivatives, and its adjoint is derived via the divergence theorem, yielding a concise geometric form of the Fokker-Planck equation. In the Ito formulation, a diffusion tensor field is introduced to generalize the Euclidean diffusion matrix, and a tensor-field-based analysis establishes an intrinsic double-divergence representation of the Fokker-Planck equation. The proposed framework provides a globally valid and geometrically consistent interpretation of diffusion and probability transport on Riemannian manifolds, supported by compact and intuitive proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18320 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Tensor Field Formulation of the Fokker-Planck Equation on Riemannian Manifolds Lee, Taeyoung Chirikjian, Gregory S. Probability This paper presents a global, coordinate-free formulation of the Fokker-Planck equation on Riemannian manifolds. In the Stratonovich formulation, the infinitesimal generator is expressed intrinsically through Lie derivatives, and its adjoint is derived via the divergence theorem, yielding a concise geometric form of the Fokker-Planck equation. In the Ito formulation, a diffusion tensor field is introduced to generalize the Euclidean diffusion matrix, and a tensor-field-based analysis establishes an intrinsic double-divergence representation of the Fokker-Planck equation. The proposed framework provides a globally valid and geometrically consistent interpretation of diffusion and probability transport on Riemannian manifolds, supported by compact and intuitive proofs. |
| title | Global Tensor Field Formulation of the Fokker-Planck Equation on Riemannian Manifolds |
| topic | Probability |
| url | https://arxiv.org/abs/2603.18320 |