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This paper focuses on the modeling of local acceleration and loss processes in the outer radiation belt. We begin by reviewing the statistical properties of waves that violate the first and second adiabatic invariants, leading to the loss and acceleration of high energy electrons in the outer radiation belt. After a brief description of the most commonly accepted methodology for computing quasi-linear diffusion coefficients, we present pitch-angle scattering simulations by (i) plasmaspheric hiss, (ii) a combination of plasmaspheric hiss and electromagnetic ion cyclotron (EMIC) waves, (iii) chorus waves, and (iv) a combination of chorus and EMIC waves. Simulations of the local acceleration and loss processes show that statistically, the net effect of chorus waves is acceleration at MeV energies and loss at hundreds of keV energies. The combination of three-dimensional (3D) simulations of the local processes and radial …