I asked this already in s.s.consult, but till now I ot only the answer
that it is easy.

How to estimate a Gamma process if we have for time points t_1,..,t_n
observed the values

S(t_i) + Z(t_i)

where S(t_i) is the value of the Gamma process and Z(t_i) is a
normally error term with constant variance. The Z(t_i) are independent.

Further complication is that for small t only positive values can be
observed. Here the error term has to be taken as

a truncated normal rv.

Any hints?

Thanks

Karl