  We construct analytic and numerical solutions of the Fokker-Planck equation
that arises in the context of stochastic inflation. We use these solutions to
derive necessary conditions for eternal inflation on the higher derivatives of
the scalar field potential and examine the prospects for eternal inflation in a
variety of popular models. We note similarities between the conditions needed
to avoid eternal inflation and several recently-proposed Swampland criteria,
which leads us to speculate on the possibility that the de Sitter Swampland
conjectures should be viewed as approximate consequences of a No Eternal
Inflation principle.
