The Wronskian parameterizes the class of diffusions with a given   distribution at a random time
  We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterize the class of diffusions with the same distribution as Brownian motion at an exponentially distributed time. 
Martin Klimmek
math.PR q-fin.PR