Representation of Conditional Expectations in Gaussian Analysis on Sequence Spaces
Felix Riemann
TL;DR
This paper constructs a framework for representing conditional expectations within Gaussian analysis on sequence spaces, utilizing nuclear triplets and correlation operators to derive explicit formulas.
Contribution
It introduces a new approach to explicitly represent conditional expectations in Gaussian analysis on sequence spaces using nuclear triplets and correlation operators.
Findings
Explicit formulas for conditional expectations derived
Construction of nuclear triplets of sequence spaces
Application of Bochner-Minlos theorem for Gaussian measures
Abstract
From a given nuclear triplet we construct a nuclear triplet of sequence spaces and introduce a correlated Gaussian measure via the Bochner-Minlos theorem. Considering special types of correlation operators on such sequence spaces, certain conditional expectations can be given in an explicit way.
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Taxonomy
TopicsNumerical methods in inverse problems · Statistical and numerical algorithms · Radiative Heat Transfer Studies