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Elements of a function analytic approach to probability.
Author(s) -
John Red-Horse,
Roger Ghanem
Publication year - 2008
Language(s) - English
Resource type - Reports
DOI - 10.2172/932877
Subject(s) - probabilistic logic , computer science , applied probability , context (archaeology) , probability theory , function (biology) , probabilistic analysis of algorithms , theoretical computer science , mathematics , artificial intelligence , statistics , paleontology , evolutionary biology , biology
We first provide a detailed motivation for using probability theory as a mathematical context in which to analyze engineering and scientific systems that possess uncertainties. We then present introductory notes on the function analytic approach to probabilistic analysis, emphasizing the connections to various classical deterministic mathematical analysis elements. Lastly, we describe how to use the approach as a means to augment deterministic analysis methods in a particular Hilbert space context, and thus enable a rigorous framework for commingling deterministic and probabilistic analysis tools in an application setting

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