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This chapter introduces probabilistic concepts for Banach space-valued random variables, essential for analyzing stochastic fluid-structure interaction (FSI) systems. Key topics include: While foundational probability theory (e.g., real-valued random variables) is assumed, the chapter extends these ideas to Banach spaces, emphasizing parallels. Advanced generalizations will appear in later chapters. References are provided for deeper dives into measure-theoretic probability, Brownian motion, stochastic integration, and infinite-dimensional stochastic analysis.

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Probabilistic Preliminaries

  • 章节

  • 发表日期：

    2025年

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  • Sunčica Čanić,
  • Jeffrey Kuan,
  • Boris Muha,
  • Krutika Tawri

摘要

This chapter introduces probabilistic concepts for Banach space-valued random variables, essential for analyzing stochastic fluid-structure interaction (FSI) systems. Key topics include: While foundational probability theory (e.g., real-valued random variables) is assumed, the chapter extends these ideas to Banach spaces, emphasizing parallels. Advanced generalizations will appear in later chapters. References are provided for deeper dives into measure-theoretic probability, Brownian motion, stochastic integration, and infinite-dimensional stochastic analysis.