3. Probabilistic Preliminaries

This chapter focuses on the probabilistic background necessary for analyzing stochastic fluid-structure systems, particularly those involving random quantities like fluid/structure velocity and structure displacement. It summarizes results about random variables in Banach spaces and discusses three modes of probabilistic convergence: convergence in probability, weak convergence, and convergence almost surely. The chapter also reviews classical theorems important for stochastic FSI analysis and introduces the concept of one-dimensional white noise and spacetime white noise. Additionally, it covers stochastic processes, stochastic integration, and Itô's formula, providing a foundation for understanding stochastic differential equations and their solutions. The chapter concludes with an exploration of white noise and stochastic integration, offering insights into the integration of simple functions and predictable processes against white noise.