  Starting from the deformed commutation relations \ba a_q(t) \,a_q^{\dag}(s) \
- \ q\,a_q^{\dag}(s)\,a_q(t)
  \ = \ \Gam(t-s) {\bf 1} , \quad -1\ \le \ q\ \le\ 1\nn \ea with a covariance
$\Gam(t-s)$ and a parameter $q$ varying between $-1$ and $1$, a stochastic
process is constructed which continuously deforms the classical Gaussian and
classical compound Poisson process. The moments of these distinguished
stochastic processes are identified with the Hilbert space vacuum expectation
values of products of $\hat{\om}_q (t) = \gam\,\big(\, a_q(t) + a_q^{\dag} (t)
\,\big)\;+ \; \xi\, a_q^{\dag} (t) a_q(t)$ with fixed parameters $q$, $\gam$
and $\xi$. Thereby we can interpolate between dichotomic, random matrix and
classical
  Gaussian and compound Poisson processes.
  The spectra of Hamiltonians with single-site dynamical disorder are
calculated for an exponential covariance (coloured noise) by means of the time
convolution generalized master equation formalism (TC-GME) and the
