A Synchronous coupling drives two processes with the same fresh random inputs. For example, recursions and use the same input at each step. This can reveal synchronous contraction of a random affine recursion even when independently simulated trajectories would conceal the relationship.
A Synchronous coupling drives two solutions of a stochastic differential equation by the same Brownian motion. Their difference has noise coefficient . A dissipativity inequality for the drift and this coefficient gives the mean-square contraction of synchronously coupled diffusions.
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