We present mathematical descriptions of optically stimulated luminescence (OSL) signals under linearly, hyperbolically, exponentially, and reciprocally increasing stimulation intensity for a one-trap one-recombination-center model assuming charge transfer governed by first-order kinetics. Depending on the stimulation mode, the OSL signal can be monotonically increasing, monotonically decreasing, show a peak shape, or be constant. The shape of the OSL signal is controlled by a stimulation-rate parameter (governed by the stimulation mode) and a decay-rate parameter that is proportional to the photoionization cross section. We demonstrate that the luminescence signal as a function of time under exponentially increasing-optical stimulation (EM-OSL) shows the same evolution in time as the luminescence signal under hyperbolically increasing-thermal stimulation (HM-TL). This similarity allows a new interpretation of the I?t versus In?t plot, where I is the optically stimulated luminescence intensity and t is the time. For a phosphor with several optically active traps, the OSL signal will contain several components. We show that the mathematical descriptions of the OSL signals under all stimulation modes can be related to the description of the OSL signal derived with continuous-wave (CW) stimulation. These so-called pseudo-OSL signals are helpful in a visualization of the various components in the OSL signal, where different pseudo-OSL transformations can be used to amplify different aspects. We demonstrate that the stimulation mode or pseudo-OSL transformation used has no effect on the overlap of the different OSL components. This implies that for the separation of multiple OSL components there is, in principle, no preference for a specific stimulation mode or pseudo-OSL transformation. Finally, we present a transformation related to hyperbolically modulated OSL which does facilitate separation of OSL components and may be of use for determining component specific photoionization cross sections or trapped-charge concentrations.