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2024

Causal transport on path space

Cont, Rama, Lim, Fang Rui

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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.

Causal transport on path space · Around

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