METASTABLE BEHAVIOR OF INFREQUENTLY OBSERVED, WEAKLY RANDOM, ONE-DIMENSIONAL DIFFUSION PROCESSES.

Consider the one-dimensional diffusion process X//t satisfying dX//t equals epsilon **1**/**2 dW//t minus G prime (X//t) dt where W//t is the standard Wiener process. For suitable G's with a double well (at m and M) shape and G(m) greater than G(M) and for an appropriate choice of lambda // epsilon , the scaled process X// lambda //(// epsilon //)//t, converges as epsilon approaches 0 (in an appropriate sense) to the two-state (m and M) jump process with M an absorbing state and transitions from m to M at unit rate.