  We have studied the non-Markovianity of dichotomously driven spin-boson model
in the strong coupling regime in both memory kernel and time convolutionless
master equation formulations. A strong correlation between the decay time of
the environmental correlation function and the non-zero non-Markovianity is
found in the absence of the external noise. Stochastic driving is shown to
create strong non-Markovianity when the dynamics of the system without driving
is Markovian. Also, exact analytical expressions for the trace distance
distinguishability and the non-Markovianity were obtained for the certain range
of the parameters that describe the system and its environment.
