Brownian motion on the Fubini extension space and applications
Probability
2025-12-09 v2
Abstract
We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process. Within this framework, we address two main objectives: first, we show how a system of graphon stochastic differential equations can be reformulated as a single McKean-Vlasov type equation driven by a standard Brownian motion, which significantly facilitates its analysis. Second, we establish a Girsanov theorem for a continuum of essentially pairwise independent Brownian motions.
Keywords
Cite
@article{arxiv.2509.12096,
title = {Brownian motion on the Fubini extension space and applications},
author = {Hamed Amini and Nina H. Amini and Sofiane Chalal and Gaoyue Guo},
journal= {arXiv preprint arXiv:2509.12096},
year = {2025}
}