On a sufficient condition for a diffusion process will nether reach boundaries of some interval

A one-dimensional diffusion semi-Markov process on some interval of its values is considered. Semi-Markov transition functions of the process dstisfy a second order differential equation with coefficients admitting possibility what the process stops inside this interval. In terms of coefficients of this equation some sufficient conditions are proved for the process will nether reach the left or right boundaries of this interval.