Let {Xn, n ≥ 1} be a sequence of independent and identically random variables. In 1947 Hsu and Rabbins proved that if E[X] = 0 and E[X2] < ∞, then 1 n ∑n k=1Xk converges to 0 completely. Recently, the strong convergence of weighted sums for the case of independent random variables has been discussed by Wu (1999), Hu and et. (2000, 2003) proved the complete convergence theorem for arrays of inde...

We describe efficient constructions of small probability spaces that approximate the joint distribution of general random variables. Previous work on efficient constructions concentrate on approximations of the joint distribution for the special case of identical, uniformly distributed random variables. Q 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13,

In ACT-R, some subsymbolic mechanisms can be switched on that transform ACT-R into a stochastic theory using random variables to generate choice probabilities. This paper asks for the relation between probabilities of production selection and the corresponding random variables. Starting with the assumption that choice probabilities governing production selection satisfy the requirements of Luce...