  We use the stochastic approach to investigate the measure for slow roll
eternal inflation. The probability for the universe of a given Hubble radius
can be calculated in this framework. In a solvable model, it is shown that the
probability for the universe to evolve from a state with a smaller Hubble
radius to that of a larger Hubble radius is dominated by the classical
probability without the stochastic source. While the probability for the
universe to evolve from a larger Hubble radius to a smaller one is suppressed
by $\exp(-\Delta S)$, where the de Sitter entropy $S$ arises naturally in this
stochastic approach.
