  Bernstein processes are Brownian diffusions that appear in Euclidean Quantum
Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation
associated with these processes allows one to obtain relations between
stochastic processes (Lescot-Zambrini, Progress in Probability, vols 58 and
59). More recently it has appeared that each one--factor affine interest rate
model (in the sense of Leblanc-Scaillet) could be described using such a
Bernstein process.
