A stochastic control approach to reciprocal diffusion processes

The problem of forcing a nondegenerate diffusion process to a given final configuration is considered. Using the logarithmic transformation approach developed by Fleming, it is shown that the perturbation of the drift suggested by Jamison solves an optimal stochastic control problem. Such perturbation happens to have minimum energy between all controls that bring the diffusion to the desired final distribution. A special property of the change of measure on the path-space that corresponds to the aforesaid perturbation of the drift is also shown.