Onsager-Machlup functional for stochastic lattice dynamical systems driven by time-varying noise

2024/08/16 by Xinze Zhang, Yong Li, Zhang, Xinze +1
Decision Sciences · Economics, Econometrics and Finance · #37H10 #37L60 #60H15 #82C35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #Simulation Techniques and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2408.08465

openalex publication_date 2024/08/16 · openalex created_date 2024/09/13 · openalex updated_date 2026/07/28

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 l²_ρ. 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 l²_ρ space. Additionally, we use a numerical example to illustrate our theoretical findings, based on the Euler Lagrange equation corresponding to the Onsage Machup functional.

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