We present an analysis of the electron phase space density in the Earth's outer radiation belt during three magnetically disturbed periods to determine the likely roles of inward radial diffusion and local acceleration in the energization of electrons to relativistic energies. During the recovery phase of the 9 October 1990 storm and the period of prolonged substorms between 11 and 16 September 1990, the relativistic electron phase space density increases substantially and peaks in the phase space density occur in the region 4.0 ~0.8 MeV. The peaks in the phase space density are associated with prolonged substorm activity, enhanced chorus amplitudes, and predominantly low values of the ratio between the electron plasma frequency, fpe, and the electron gyrofrequency, fce (fpe/fce < ~4). The data provide further evidence for a local wave acceleration process in addition to radial diffusion operating in the heart of the outer radiation belt. During the recovery phase of the 9 October 1990 storm the peaks are more pronounced at large M (550 MeV/G) and large Kaufmann K (0.11 G$^{^{1}\!\!/\!_{2}}$RE) than large M (700 MeV/G) and small K (0.025 G$^{^{1}\!\!/\!_{2}}$RE), which suggests that radial diffusion is more effective below about 0.7 MeV for 5.0 < L* < 5.5 during this period. At low M (M ≤ 250 MeV/G), corresponding to energies, E < ~0.8 MeV, there is no evidence for a peak in phase space density and the data are more consistent with inward radial diffusion and losses to the atmosphere by pitch angle scattering. During the 26 August 1990 storm there is a net loss in the relativistic electron phase space density for 3.3 < L* < 6.0. At low M (M ≤ 250 MeV/G) the phase space density decreases by almost a constant factor and the gradient remains positive for all L*, but at high M (M ≥ 550 MeV/G) the decrease in phase space density is greater at larger L* and the gradient changes from positive to negative. The data show that it is possible to have inward radial diffusion at low energies and outward radial diffusion at higher energies, which would fill the outer radiation belt.