A central limit theorem for families of stochastic processes indexed by a small average step size parameter,and some applications to learning models

Let > 0 be a measure of the average step size of a stochastic process {p_n⁽⁾ }_n=1⁽⁾. Conditions are given under whichp_n⁽⁾ is approximately normally distributed whenn is large and is small. This result is applied to a number of learning models where is a learning rate parameter andp_n⁽⁾ is the probability that the subject makes a certain response on thenth experimental trial. Both linear and stimulus sampling models are considered.