Stochastic dynamics on product manifolds: twenty five years after
UDC 519.21; 517.9 We consider an infinite system of stochastic differential equations in a compact manifold $\mathcal{M}.$ The equations are labeled by vertices of a geometric graph with unbounded vertex degrees and coupled via the nearest neighbor interaction. We prove the global existence and uniq...
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| Date: | 2026 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8411 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 519.21; 517.9
We consider an infinite system of stochastic differential equations in a compact manifold $\mathcal{M}.$ The equations are labeled by vertices of a geometric graph with unbounded vertex degrees and coupled via the nearest neighbor interaction. We prove the global existence and uniqueness of strong solutions and construct in this way the stochastic dynamics associated with Gibbs measures that describes equilibrium states of a (quenched) system of particles with positions, which form a typical realization of a Poisson or Gibbs point process in $\mathbb{R}^{d}.$ |
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| DOI: | 10.3842/umzh.v77i4.8411 |