Limit theorem for randomly indexed sequence of random processes

TL;DR

This paper establishes a limit theorem for sequences of random processes with random indices, assuming independence between the index sequences and the processes, and provides an estimate of the convergence rate.

Contribution

It introduces a new limit theorem for randomly indexed random processes and offers an estimation of the convergence rate under independence assumptions.

Findings

Proved the limit theorem for randomly indexed sequences of random processes.

Derived an estimate for the convergence rate.

Assumed independence between index sequences and processes.

Abstract

In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.