A simplified variational characterization of Schrödinger processes

The variational problem E[1/2 ∫T0(βt−A(t,Xt))2 dt −∫T0c(t,Xt)dt]=min, where βt is the drift process of a diffusion process with unit diffusion coefficient and given initial and final distributions, A is a given vector field, and c is a given scalar field, is considered. It is shown that the solution is given by a certain Markovian diffusion process, which (in the case A=0, c=0) first was investigated by Schrodinger (Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 1931, 144).