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The article shows a bridge representation for the joint density of a systemof stochastic processes consisting of a Brownian motion with drift coupled witha correlated fractional Brownian motion with drift. As a result, a small timeapproximation of the joint density is readily obtained by substituting theconditional expectation under the bridge measure by a single path: themodal-path from the initial point to the terminal point.

Bridge representation and modal-path approximation