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Representations of Conditional Means
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M. M. Rao
Published/Copyright:
February 25, 2010
Abstract
A unified treatment of integral representations of conditional expectations, in terms of Bochner integrals, with specializations to Gaussian conditioning, is given. The integrals in the latter have deterministic kernels. Difficulties in actual calculations of (even regular) conditional probabilities, and the inadequacy of methods related to L'Hospital's procedures, are exemplified. Limitations of the methods used and some new problems for investigation are indicated.
Key words and phrases:: Bochner's integral representation; deterministic kernels; Kac–Slepian paradox; Bochner's boundedness principle
Received: 2000-04-04
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
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- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
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Keywords for this article
Bochner's integral representation;
deterministic kernels;
Kac–Slepian paradox;
Bochner's boundedness principle
Articles in the same Issue
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
