  Recent experiments have demonstrated the feasibility of exploiting spectral
singularities in open quantum and wave systems, so-called exceptional points,
for sensors with strongly enhanced sensitivity. Here, we study theoretically
the influence of classical parametric noise on the performance of such sensors.
Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the
resolvability of frequency splittings and the dynamical stability of the
sensor, and show that these properties are interrelated. Of central importance
are the different features of exceptional points in the spectra of the
Hamiltonian and the corresponding Liouvillian. Two realistic examples, a
parity-time-symmetric dimer and a whispering-gallery microcavity with
asymmetric backscattering, illustrate the findings.
