A nontrivial scaling limit for multiscale Markov chains
The authors consider Markov chains with two variables characterized by two different timescales. They show that in a suitable scaling limit the presence of fast and slow variables leads to a deterministic dynamics, radically different from the mean field limit obtained by rescaling in a Markov chain with a singe variable. The authors also analyze an application to a model of a molecular motor. The obtained results are put in connection with the phenomenon of self-induced stochastic resonance [\textit{M. I. Freidlin}, J. Stat. Phys. 103, No. 1--2, 283--300 (2001; Zbl 1019.82008)], where matching between two quite different timescales leads to important effects driven by noise in the coherent dynamics.
scientific article; zbMATH DE number 5146516