Limit theorems for random processes with random time substitution

TL;DR

This paper establishes sufficient conditions for the convergence of sequences of random processes with random time substitution in the Skorokhod space, advancing understanding of their limiting behavior.

Contribution

It provides new theoretical conditions ensuring convergence of such processes, filling gaps in the existing convergence criteria.

Findings

Derived sufficient conditions for convergence in Skorokhod space

Applied to processes with random time changes

Enhanced theoretical framework for stochastic process convergence

Abstract

In this paper the sufficient conditions for convergence in Skorokhod space $D[0,1]$ of sequence of random processes with random time substitution are obtained.