Elements of a function analytic approach to probability.

Ghanem, Roger Georges (University of Southern California, Los Angeles, CA) ; Red-Horse, John Robert

Sandia National Laboratories

关键词: Probability;    Probability Theory.;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Uncertainty-Mathematical Models.;    Calculation Methods Uncertainty-Mathematical Models.;   

DOI  :  10.2172/932877
RP-ID  :  SAND2008-0963
RP-ID  :  AC04-94AL85000
RP-ID  :  932877

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.