Diffusion processes in one dimension

in a finite or infinite interval r1<x<r2. Recently 2 the theory of semigroups of transformations was used to formulate the integration problem and to define the notion of lateral conditions. It will now be shown that the semi-groups constructed in 2 permit us to describe the totality of all stochastic processes connected with (1.1). To each there corresponds a forward, or Fokker-Planck, equation. It reduces only in simplest cases to the familiar adjoint