We have computed the path-integrated gain of parallel propagating whistlers driven unstable by an anisotropic distribution of relativistic electrons in the stable trapping region of Jupiter's inner magnetosphere. The requirement that a gina of three e foldings of power balance the power lost by imperfect reflection along the flux tube sets a stably trapped flux of electrons J*=4¿1010 L-4 cm-2 s-1, which is close to the nonrelativistic result. Comparison with measurements shows that observed fluxes are near the stably trapped limit, which suggests that whistler wave intensities may be high enough to cause significant diffusion of electrons accounting for the observed reduction of phase space densities. A crude estimate of fluctuation intensity of IB=1.5¿10-18(&OHgr;ce/&ohgr;)2L&agr;-2 W m-2 Hz-1 as a lower limit for a diffusion coefficient modeled as DLL=10-10L&agr; s-1.