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In this chapter, we establish weak convergence in the space \(\mathbb {C}[0,1]\) for the continuous time case and in the space \(\mathbb {D}[0,1]\) for the discrete time case of normalized stochastic processes. These processes are generated by Toeplitz type quadratic functionals of Gaussian and Lévy-driven linear stationary processes that exhibit long-range dependence. We have established both central and non-central functional limit theorems.

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Functional Limit Theorems for Toeplitz Processes

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  • 发表日期：

    2025年

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  • Mamikon S. Ginovyan

摘要

In this chapter, we establish weak convergence in the space \(\mathbb {C}[0,1]\) for the continuous time case and in the space \(\mathbb {D}[0,1]\) for the discrete time case of normalized stochastic processes. These processes are generated by Toeplitz type quadratic functionals of Gaussian and Lévy-driven linear stationary processes that exhibit long-range dependence. We have established both central and non-central functional limit theorems.