The convergence of the random lines defined by observations of a stochastic process

Abstract

We deal with independent random variables which are the values of a stochastic process taken at random points in time. So we have random variables depending upon a random parameter. We obtain the conditions providing the weak convergence of random lines defined by sums or maxima or bilinear forms of these random variables for almost all values of the parameter, to one and the same stochastic process. These limit stochastic processes are described.