Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise
Abstract
This paper investigates the Onsager-Machlup functional of stochastic lattice dynamical systems (SLDSs) driven by time-varying noise. We extend the Onsager-Machlup functional from finite-dimensional to infinite-dimensional systems, and from constant to time-varying diffusion coefficients. We first verify the existence and uniqueness of general SLDS solutions in the infinite sequence weighted space $l^2_{\rho}$. Building on this foundation, we employ techniques such as the infinite-dimensional Girsanov transform, Karhunen-Loève expansion, and probability estimation of Brownian motion balls to derive the Onsager-Machlup functionals for SLDSs in $l^2_{\rho}$ space. Additionally, we use a numerical example to illustrate our theoretical findings, based on the Euler Lagrange equation corresponding to the Onsage Machup functional.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.08465
- arXiv:
- arXiv:2408.08465
- Bibcode:
- 2024arXiv240808465Z
- Keywords:
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- Mathematics - Probability;
- Mathematics - Classical Analysis and ODEs;
- 82C35;
- 37L60;
- 60H15;
- 37H10
- E-Print:
- 25 pages, 3 figures