On transformations of linear diffusions into continuous state branching (Q1070661)

The author presents three examples of one-dimensional diffusions whose backward equations may be transformed into those of the continuous state branching process with immigration or emigration, thus obtaining the fundamental solution of the original process. The method of proof consists in presenting explicit transformations. The first example is the Bessel process. The second is Girsanov's example of non-uniqueness of solutions of stochastic differential equations \(dX(t)=X^ a(t)dB(t)\), where B(t) is Brownian motion (non-uniqueness is for \(0\leq a<1/2\), but other cases are studied here). The third example is the family of one-dimensional self-similar diffusions on the positive half line.