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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 194–198 (Mi tvp311)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Hölder equality for conditional expectations with application to linear monotone operators

G. Di Nunno

Dipartimento di Matematica dell'Università di Pavia

Abstract: In a standard space $L_p=L_p(\Omega,\mathfrak{A},P)$, $1\le p<\infty$, for a given factor $f$ and a $\sigma$-algebra $\mathfrak{B}\subseteq\mathfrak{A} $, a certain criterion is derived for a conditional expectation $x(X)=E(Xf | \mathfrak{B})$ to represent a continuous linear operator over $X\in L_p$. As an application, the above representation (with the corresponding factor $f\ge 0$) is considered for a general linear monotone operator $x(X)$, $X\in K$, given on an arbitrary subcone $K\subseteq L_p^+ $ in $L_p^+ =\{X\in L_p:X\ge 0\}$.

Keywords: conditional expectations, Hölder inequality, linear monotone operators, linear monotone extensions.

DOI: https://doi.org/10.4213/tvp311

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English version:
Theory of Probability and its Applications, 2004, 48:1, 177–181

Bibliographic databases:

Received: 09.07.2000
Revised: 14.05.2002
Language:

Citation: G. Di Nunno, “Hölder equality for conditional expectations with application to linear monotone operators”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 194–198; Theory Probab. Appl., 48:1 (2004), 177–181

Citation in format AMSBIB
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\jour Theory Probab. Appl.
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Albeverio S., Di Nunno G., Rozanov Yu.A., “Price operators analysis in $L_p$-spaces”, Acta Appl. Math., 89:1-3 (2005), 85–108  crossref  mathscinet  zmath  isi  scopus
    2. Di Nunno G., Eide I.B., “Lower and Upper Bounds of Martingale Measure Densities in Continuous Time Markets”, Mathematical Finance, 21:3 (2011), 475–492  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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