Mean stochastic comparison of diffusions

Summary Stochastic bounds are derived for one dimensional diffusions (and somewhat more general random processes) by dominating one process pathwise by a convex combination of other processes. The method permits comparison of diffusions with different diffusion coefficients. One interpretation of the bounds is that an optimal control is identified for certain diffusions with controlled drift and diffusion coefficients, when the reward function is convex. An example is given to show how the bounds and the Liapunov function technique can be applied to yield bounds for multidimensional diffusions.This work was supported by the Office of Naval Research under Contract N00014-82-K-0359 and the U.S. Army Research Office under Contract DAAG29-82-K-0091 (administered through the University of California at Berkeley).