  We study the Quantum Zeno Effect (QZE) induced by continuous partial
measurement in the presence of short-correlated noise in the system
Hamiltonian. We study the survival probability and the onset of the QZE as a
function of the measurement strength, and find that, depending on the noise
parameters, the quantum Zeno effect can be enhanced or suppressed by the noise
in different regions of the parameter space. Notably, the conditions for the
enhancement of the QZE are different when determined by the short-time or
long-time behavior of the survival probability, or by the measurement strength
marking the onset of the quantum Zeno regime.
