Convergence of Random Elements

Mircea D. Grigoriu
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Mircea D. Grigoriu: Cornell University

Chapter Chapter 4 in Numerical Methods for Extreme Responses of Dynamical Systems, 2025, pp 117-146 from Springer

Abstract: Abstract Concepts used extensively in the subsequent chapters of the book are reviewed and illustrated by simple examples. The review includes linear, normed, Hilbert, and metric spaces, topology induced on metric spaces by their metrics, σ $$\sigma $$ -fields on metric spaces, the space of real-valued continuous functions C[0, τ $$\tau $$ ] defined on bounded time intervals [0, τ $$\tau $$ ], random processes with continuous paths, convergence in C[0, τ $$\tau $$ ], and continuous mapping theorem, an essential tool for characterizing extremes of target processes by those of their FD models.

Keywords: Continuous mapping theorem; Metric space; Modes of convergence for random processes; Sequence of FD models; Space of continuous functions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-75023-6_4

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DOI: 10.1007/978-3-031-75023-6_4

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