The adapted 2-Wasserstein distance between fractional Brownian motions equals the Hilbert-Schmidt distance between their Molchan-Golosov kernels, attained by the synchronous coupling.
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A transfer principle for computing the adapted Wasserstein distance between stochastic processes
The adapted 2-Wasserstein distance between fractional Brownian motions equals the Hilbert-Schmidt distance between their Molchan-Golosov kernels, attained by the synchronous coupling.