Traversing the Schroedinger Bridge strait: Robert Fortet's marvelous proof redux

Understand

In the early 1930's, Erwin Schroedinger, motivated by his quest for a more classical formulation of quantum mechanics, posed a large deviation problem for a cloud of independent Brownian particles.

• He showed that the solution to the problem could be obtained trough a system of two linear equations with nonlinear coupling at the boundary (Schr\"odinger system).
• Existence and uniqueness for such a system, which represents a sort of bottleneck for the problem, was first established by R.
• Fortet in 1938/40 under rather general assumptions by proving convergence of an ingenious but complex approximation method.