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We studied the spin-transfer switching probability (Psw) in giant magnetoresistance (GMR) device with perpendicular magnetizations using short nanosecond and sub-nanosecond current pulses. A switching time of 510 picoseconds was achieved with the application of 7.5 mA, which is 4.3 times larger than the critical current at 0 K, without the application of an assisting magnetic field. Experiments with longer pulses revealed an exponential decay of the nonswitching probability (1-Psw) as a function of pulse width. Extrapolation of the results predicts an error rate of 10-19 for a pulse width of about 4.8 ns. To understand the observed pulse width dependence of Psw, we developed a formula using a macro spin model for the perpendicular magnetization system which includes the influence of thermal fluctuations in the initial magnetization direction of the free layer. The formula easily reproduces the qualitative nature of the observed Psw distributions in all time ranges.