On the strong uniqueness of a solution to singular stochastic differential equations

Gerold Alsmeyer, Andrea Winkler
Theory of Stochastic Processes
Vol.18 (34), no.1, 2012, pp.3-44
Glass-forming systems, characterized by a highly disordered energy landscape, have been studied in physics by a simulation-based state space aggregation. Choosing a path-independent approach within the framework of finite Markov chains, this article provides an aggregation procedure which, at an appropriate aggregation level, leads to the definition of certain metastates, called metabasins in Physics (for their properties see the Introduction). Roughly speaking, this will be the finest aggregation such that transitions back to an already visited (meta-)state are very unlikely within a moderate time frame.