Functional central limit theorems for U-statistics of beta-mixing data

Key Points

• This research explores the convergence properties of partial sum processes derived from beta-mixing sequences of random variables.
• Analyzed convergence in the space of continuous functions and Hölder spaces.
• Considered strictly stationary beta-mixing sequences with conditions approaching optimality.
• Established criteria for convergence that are nearly optimal.
• Demonstrated that convergence occurs in specified functional spaces.