Limits of relative entropies associated with weakly interacting particle systems

作者：Budhiraja Amarjit^*; Dupuis Paul; Fischer Markus; Ramanan Kavita

来源：Electronic Journal of Probability, 2015, 20(0): 1-22.

DOI：10.1214/EJP.v20-4003

• Nonlinear Markov processes
• weakly interacting particle systems
• interacting Markov chains
• mean field limit
• stability
• metastability
• Lyapunov functions
• relative entropy
• large deviations

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].

• 出版日期2015-8-4