  Dynamical decoupling is an important tool to counter decoherence and
dissipation effects in quantum systems originating from environmental
interactions. It has been used successfully in many experiments; however, there
is still a gap between fidelity improvements achieved in practice compared to
theoretical predictions. We propose a model for imperfect dynamical decoupling
based on a stochastic Ito differential equation which could explain the
observed gap. We discuss the impact of our model on the time evolution of
various quantum systems in finite- and infinite-dimensional Hilbert spaces.
Analytical results are given for the limit of continuous control, whereas we
present numerical simulations and upper bounds for the case of finite control.
