The relationship between pump-probe transients and the transition frequency correlation function, M(t), is examined. Calculations of pump-probe transients are carried out with a full-quantum expression for a displaced harmonic oscillator coupled to a heat bath. Pump-probe transients for a slowly decaying, overdamped, Brownian oscillator are shown to resemble a power series in M(t), where the slowest time scale is always equal to the slowest decay in M(t). This equality is consistent with a semiclassical model of pump-probe and valid over the full range of temperature, pulse duration, and detuning explored. The contribution of time scales faster than M(t) to the pump-probe transient increases with increasing temperature, pulse duration, and detuning of the pulse center frequency below resonance. Pump-probe transients for a critically damped oscillator that decays on a femtosecond time scale also have faster early time decay at higher temperatures. Based on these calculations a bootstrap method is suggested for extracting M(t) from pump-probe data starting with the slowest decay. Comparisons are made between simulations of pump-probe and three pulse echo peak shift (3PEPS) transients for a single oscillator and for multiple oscillator systems. Additional fast relaxations similar to those in pump-probe are also present in the 3PEPS transients. For the models investigated, pump-probe is comparable to 3PEPS for the extraction of M(t). (C) 2003 American Institute of Physics.