  We study a noisy oscillator with pulse delayed feedback, theoretically and in
an electronic experimental implementation. Without noise, this system has
multiple stable periodic regimes. We consider two types of noise: i) phase
noise acting on the oscillator state variable and ii) stochastic fluctuations
of the coupling delay. For both types of stochastic perturbations the system
hops between the deterministic regimes, but it shows dramatically different
scaling properties for different types of noise. The robustness to conventional
phase noise increases with coupling strength. However for stochastic variations
in the coupling delay, the lifetimes decrease exponentially with the coupling
strength. We provide an analytic explanation for these scaling properties in a
linearised model. Our findings thus indicate that the robustness of a system to
stochastic perturbations strongly depends on the nature of these perturbations.
