This book is intended to provide a treatment of the theory and applications of Stochastic Neural Networks,that is networks able to learn random processes from experience, on the basis of recent developments on this subject. The mathematical frameworks on which the theory is founded embrace the approximation of non-random functions as well as the theory of stochastic processes. The networks so defined constitute an original and very promising model of human brain neural activity consistent with the need of learning from a stochastic environment. Moreover, the problem of speech modeling, both for synthesis and recognition, is faced as concrete and significant application in the field of artificial intelligence of the theory is presented.