2024/12/04 by Rama Cont, Cont, Rama, Fang Rui Lim +1 · 2 citations
Physics and Astronomy · #49Q22 #60H05 #60H10 #FOS: Mathematics #Orbital Angular Momentum in Optics #Probability (math.PR) #Quantum Mechanics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2412.02948
openalex publication_date 2024/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study properties of causal couplings for probability measures on the space of continuous functions. We first provide a characterization of bicausal couplings between weak solutions of stochastic differential equations. We then provide a complete description of all such bicausal Monge couplings. In particular, we show that bicausal Monge couplings of d-dimensional Wiener measures are induced by stochastic integrals of rotation-valued integrands. As an application, we give necessary and sufficient conditions for bicausal couplings to be induced by Monge maps and show that such bicausal Monge transports are dense in the set of bicausal couplings between laws of SDEs with regular coefficients.