In many ultrashort-laser-pulse experiments the field is transform limi
ted, and under these conditions it is usually assumed that the stochas
tic nature of the field can be ignored in the interpretation of experi
mental data. We theoretically consider the 3 + 2 photoionization of xe
non, using a pulsed stochastic field. Our results show that the held's
stochastic nature always has an effect on the sc Stark shift modifica
tion factor Re(M), no matter what the pulse width, and that a short-pu
lse approximation to Re(M) can require a Fourier-transform bandwidth 1
000 times larger than the laser's intrinsic (cw) spectral width.