Limits of relative entropies associated with weakly interacting particle systems

Amarjit Budhiraja; Paul Dupuis; Markus Fischer; Kavita Ramanan

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arXiv · 1412.5553

Limits of relative entropies associated with weakly interacting particle systems

Amarjit Budhiraja·Paul Dupuis·Markus Fischer·Kavita Ramanan

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Abstract

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

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Amarjit Budhiraja, Paul Dupuis, Markus Fischer, Kavita Ramanan. 2014-12-17. Limits of relative entropies associated with weakly interacting particle systems. https://arxiv.org/abs/1412.5553

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