  We develop methods for the solution of inhomogeneous Robin type boundary
value problems (BVPs) that arise for certain linear parabolic Partial
Differential Equations (PDEs) on a half line, as well as a second order
generalisation. We are able to obtain non-standard solutions to equations
arising in a range of areas, including mathematical finance, stochastic
analysis, hyperbolic geometry and mathematical physics. Our approach uses the
odd and even Hilbert transforms. The solutions we obtain and the method itself
seem to be new.
