  We discuss a few mathematical aspects of random dynamical decoupling, a key
tool procedure in quantum information theory. In particular, we place it in the
context of discrete stochastic processes, limit theorems and CPT semigroups on
matrix algebras. We obtain precise analytical expressions for expectation and
variance of the density matrix and fidelity over time in the continuum-time
limit depending on the system Lindbladian, which then lead to rough short-time
estimates depending only on certain coupling strengths. We prove that dynamical
decoupling does not work in the case of intrinsic (i.e., not
environment-induced) decoherence, and together with the above-mentioned
estimates this yields a novel method of partially identifying intrinsic
decoherence.
