The nuclei of starburst galaxies are unique sources of high-energy radiation where ideal conditions
for cosmic ray acceleration and confinement might be achieved. We investigate the conditions
for effective cosmic ray confinement by modelling the transport accounting for diffusion
and advection, and we study the implications of such confinement in terms of multifrequency
emission and production of high-energy neutrinos. Both primary and secondary electrons, as
well as electron-positron pairs produced by gamma ray absorption inside these regions are taken
into account. Electrons and positrons produced as secondary products of hadronic interactions
are found to be responsible for most of the emission of leptonic origin. In particular, secondary
electrons produce an extended synchrotron emission of hard X-rays that represent a remarkable
signature of hadronic processes, potentially accessible to current and future observations in the
X-ray band. We also apply for the first time our detailed model to study the starburst contribution
to the diffuse gamma-ray and neutrino fluxes observed by Fermi-LAT and IceCube. In order to
assess such contribution we adopt a redshift number density of starburst-like objects based on the
infrared luminosity function inferred by Herschel observations and we take into account the effect
of the electromagnetic cascade in the intergalactic medium.