Use of one-parameter group transformations is made to obtain the transition p.d.f. of a Feller process confined between the origin and a hyperbolic-type boundary. Such a procedure, previously used by Bluman and Cole (cf., for instance, ), although useful for dealing with one-dimensional diffusion processes restricted between time-varying boundaries, does not appear to have been sufficiently exploited to obtain solutions to the diffusion equations associated to continuous Markov processes.
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