Limits of relative entropies associated with weakly interacting particle\n systems

2014/12/17 by Amarjit Budhiraja, Paul Dupuis, Budhiraja, Amarjit +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1412.5553

openalex publication_date 2014/12/17 · openalex created_date 2022/10/13 · openalex updated_date 2026/07/28

Abstract

The limits of scaled relative entropies between probability distributions\nassociated with N-particle weakly interacting Markov processes are considered.\nThe convergence of such scaled relative entropies is established in various\nsettings. The analysis is motivated by the role relative entropy plays as a\nLyapunov function for the (linear) Kolmogorov forward equation associated with\nan ergodic Markov process, and Lyapunov function properties of these scaling\nlimits with respect to nonlinear finite-state Markov processes are studied in\nthe companion paper [6].\n

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