Optimal control of one dimensional non-conservative quasi-diffusion processes

An extension of the work of P. Mandl concerning the optimal control of time-homogeneous diffusion processes in one dimension is given. Instead of a classical second order differential operator as infinitesimal generator, Feller's generalized differential operator D_mD⁺_p with a possibly nondecreasing weight function m is used. In this manner an optimal control of a wider class of one dimensional Marcov processes-including diffusions as well as birth and death processes-is realized.