A quantitative evaluation of the main physical processes in Earth's radiation belts has been difficult because of the broad-spectrum of timescales of the physical processes (milliseconds to several minutes). This thesis presents the K2 model, which incorporates a wide spectrum of timescales by combining Stochastic Differential Equation (SDE) methods into an otherwise Magnetohydrodynamics (MHD)-particle framework. We present the simulation results of March 17, 2013 event and show the capabilities of the K2 model. Additionally, an important spacecraft under-sampling of the simulation results is observed using NASA Van Allen Probes spacecraft orbits. A separate guiding-center code is constructed to investigate the quasilinear diffusion limit of the radial transport produced by ultra low-frequency waves contained in the MHD fields. We show that given sufficient phase randomization, the particle motion is diffusive. It is observed numerically that the addition of the electric and electromagnetic diffusion coefficients is equal to the combined diffusion coefficient.