Construction of Gaussian (OU) processes to represent fluctuating, trial-by-trial firing rate of a pool of weakly correlated MT neurons (Bair et al. 2001; Zohary et al. 1994). As in Mazurek and Shadlen (2002), these motion sensitive neurons provide direct input to our model integrator circuits. Simulated spike trains from weakly correlated, direction selective pools of neurons are shown as a rastergram. All spikes before time t, a sum over the jth spike from the ith neuron, for all i and j, are convolved with an exponential filter, and then summed to create a continuous stochastic output (right); here, H(t) is the Heaviside function. We approximated this output by a simpler Gaussian (OU) process to simplify numerical and analytical computations that follow.