Divergence-Kernel method for scores of random systems
Probability
2025-07-08 v1 Numerical Analysis
Dynamical Systems
Numerical Analysis
Optimization and Control
Abstract
We derive the divergence-kernel formula for the scores of random dynamical systems, then formally pass to the continuous-time limit of SDEs. Our formula works for multiplicative noise systems over any period of time; it does not require hyperbolicity. We also consider several special cases: (1) for additive noise, we give a pure kernel formula; (2) for short-time, we give a pure divergence formula; (3) we give a formula which does not involve scores of the initial distribution. Based on the new formula, we derive a pathwise Monte-Carlo algorithm for scores, and demonstrate it on the 40-dimensional Lorenz 96 system with multiplicative noise.
Cite
@article{arxiv.2507.04035,
title = {Divergence-Kernel method for scores of random systems},
author = {Angxiu Ni},
journal= {arXiv preprint arXiv:2507.04035},
year = {2025}
}
Comments
22 pages