[en] We study high-energy neutrino and cosmic-ray (CR) emission from the cores of low-luminosity active galactic nuclei (LLAGN). In LLAGN, the thermalization of particles is expected to be incomplete in radiatively inefficient accretion flows (RIAF), allowing the existence of non-thermal particles. In this work, assuming stochastic particle acceleration due to turbulence in RIAFs, we solve the Fokker–Planck equation and calculate spectra of escaping neutrinos and CRs. The RIAF in LLAGN can emit CR protons with $\gtrsim <!--\; ???\; -->10$ PeV energies and TeV–PeV neutrinos generated via pp and/or $p\mathrm{\gamma <!--\; ??\; -->}$ reactions. We find that, if ∼1% of the accretion luminosity is carried away by non-thermal ions, the diffuse neutrino intensity from the cores of LLAGN may be as high as $E_{\mathrm{\nu <!--\; ??\; -->}}^2{\mathrm{\Phi <!--\; ??\; -->}}_{\mathrm{\nu <!--\; ??\; -->}}\sim <!--\; ???\; -->3\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->8}\mathrm{G}\mathrm{e}\mathrm{V}{\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->2}{\mathrm{s}}^{-<!--\; ???\; -->1}{\mathrm{s}\mathrm{r}}^{-<!--\; ???\; -->1}$, which can be compatible with the observed IceCube data. This result does not contradict either of the diffuse gamma-ray background observed by Fermi or observed diffuse CR flux. Our model suggests that, although very-high-energy gamma-rays may not escape, radio-quiet active galactic nuclei with RIAFs can emit GeV gamma-rays, which could be used for testing the model. We also calculate the neutron luminosity from RIAFs of LLAGN, and discuss a strong constraint on the model of jet mass loading mediated by neutrons from the diffuse neutrino observation.