Year: 2026
Type: article
Abstract: . We study coarse-graining methods for stochastic differential equations. In particular we consider averaging and a type of projection operator method, sometimes referred to as effective dynamic via conditional expectations. The projection method (PM) we consider is related to the “mimicking marginals” coarse-graining approach proposed by Gyöngy. The first contribution of this paper is to provide further theoretical background for the PM and a rigorous link to the Gyöngy method. Moreover, we compare PM and averaging. While averaging applies to systems with time-scale separation, the PM can in principle be applied irrespective of this. It is sometimes tacitly assumed that the two methods coincide in the limit of perfect scale separation. The second contribution of this paper is to make this statement precise, provide sufficient conditions under which these two methods coincide and then show—via examples and counterexamples—that this needs not be the case.
DOI: 10.1137/25m1770114
Authors: Hong Duong, Carsten Hartmann, Michela Ottobre
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Evolutionary Game Theory Under Uncertainty, SFB 1114: Skalenkaskaden in komplexen Systemen, Verbundvorhaben EIZ: Energie-Innovationszentrum der Brandenburgischen Technischen Universität Cottbus-Senftenberg, Teilvorhaben: Energy Economics Lab, Electric Power Systems Lab, Control Systems and Cyber Security Lab, Energy Storage and Conversion Lab, High Power Grid Converter Lab, Scientific Computing Lab, G651204332
OpenAlex ID: W7169642381