Using Divine's (1976) model for the observed energetic electron intensity distribution in the inner Jovian magnetosphere to calculate phase space density profiles, we estimate the loss term for steady state radial diffusion in whcih the first and second adiabatic invariants are conserved, namely L=L2∂/∂L (D0Ln-2∂f/∂L), where a radial diffusion coefficient of the form DLL=D0Ln is assumed. The assumption that all of the losses are due to precipitation into the ionosphere yields an upper limit for the precipitation flux at ionospheric altitudes. We find that for a given electron energy, the ionospheric precipitation flux rises steeply with L between ~3 and ~10. For example, the precipitation flux of 1 MeV electrons is ~105 cm-2 s-1 MeV-1 at L=9.1 but diminishes to ~50 cm-2 s-1 MeV-1 at L=3.6. Using our calculated precipitation profiles, we estimate the total energy deposition in the ionosphere due to the precipitating particles and find it to be less than a few tenths f an erg cm-2 s-1, which is of the same order as the energy deposited by energetic (Ee>100 keV) electrons electrons during the recovery phase of a terrestrial geomagnetic storm. The estimated flux of X rays that would be produced by bremsstrahlung of the precipitating particles is several orders of magnitude below the observational upper limit at earth. We further estimate that the total rate at which electrons with first invariants between a few tens and a few thousands of MeV/Gauss are lost from the range 2.8<L<10.2 is ~1024 electrons/s. This is of the same order as the rate at which electrons of this energy range diffusively enter this region, indicating that the loss processes are quite efficient. Finally, we estimate the lifetimes of the particles against precipitation and find them to be more than two orders of magnitude longer than the minimum lifetime against strong pitch angle diffusion. The losses therefore occur near the weak limit. We discuss the effects of varying D0 and n and of the distortion of the magnetic field at the ionospheric level due to higher order moments.