Weak convergence of random polygonal lines to a Gaussian process (Q2571508)

The author considers a random step-line process constructed from partial sums of random variables with random replacement, where the array of random variables is rowwise independent and satisfies a Lindeberg-Feller condition, and the replacements are modelled by multiplication of indicators of certain events coming from a different probability space. Under certain conditions it is shown that the resulting random polygonal lines converge in distribution to a centered Gaussian process in the space of continuous functions and almost surely with respect to the replacements' probability space. In a particular case of replacements the limit process is the standard Ornstein-Uhlenbeck process.