Brownian motion on Fubini extensions and applications
Abstract
The aim of this paper is to establish a certain equivalence between a Brownian motion on a Fubini extension space and a collection of essentially pairwise independent Brownian motions on the marginal sample spaces. This equivalence allows us to state a Girsanov theorem that preserves pairwise independence and to formulate graphon stochastic differential equations as a single McKean-Vlasov type equation driven by a standard Brownian motion.
Fields of Study & Subjects
Stochastic processes and financial applications
Economic theories and models
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- HAL (Le Centre pour la Communication Scientifique Directe)
- Publication date
- 31 March 2026
- Language
- EN
- Document type
- Preprint