  Stellar core collapse events are expected to produce gravitational waves via
several mechanisms, most of which are not yet fully understood due to the
current limitations in the numerical simulations of these events. In this
paper, we begin with an empirical functional form that fits the
gravitational-wave spectra from existing simulations of stellar core collapse
and integrate over all collapse events in the universe to estimate the
resulting stochastic gravitational-wave background. We then use a Gaussian
functional form to separately fit and model a low-frequency peak in the
core-collapse strain spectra, which likely occurs due to prompt convection. We
systematically study the parameter space of both models, as well as the
combined case, and investigate their detectability by upcoming
gravitational-wave detectors, such as Advanced LIGO and Einstein Telescope.
Assuming realistic formation rates for progenitors of core-collapse supernovae,
our results indicate that both models are 2--4 orders of magnitude below the
expected sensitivity of Advanced LIGO, and 1--2 orders of magnitude below that
of the Einstein Telescope.
