The Krein condition for the moment problem: appendix A

Henrik Laurberg Pedersen

doi:10.1239/jap/1127322032

The Krein condition for the moment problem: appendix A

5 Citations (Scopus)

Abstract

In this paper, we describe a class of Wiener functionals that are `indeterminate by their moments', that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.

Original language	English
Journal	Journal of Applied Probability
Volume	42
Issue number	3
Pages (from-to)	857-860
Number of pages	4
ISSN	0021-9002
DOIs	https://doi.org/10.1239/jap/1127322032
Publication status	Published - 2005

Keywords

Former LIFE faculty
indeterminate moment problem
harmonic function
harmonic estimation

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10.1239/jap/1127322032

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title = "The Krein condition for the moment problem: appendix A",

abstract = "In this paper, we describe a class of Wiener functionals that are `indeterminate by their moments', that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.",

keywords = "Former LIFE faculty, indeterminate moment problem, harmonic function, harmonic estimation",

author = "Pedersen, {Henrik Laurberg}",

note = "Appendix A in {"}The Moment Problem for Some Weiner Functionals: Corrections to Previous Proofs (with and Appendix by H.L. Pedersen){"}, by Per H{\"o}rfelt, Chalmers University of Technology",

year = "2005",

doi = "10.1239/jap/1127322032",

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pages = "857--860",

journal = "Journal of Applied Probability",

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T1 - The Krein condition for the moment problem

T2 - appendix A

AU - Pedersen, Henrik Laurberg

N1 - Appendix A in "The Moment Problem for Some Weiner Functionals: Corrections to Previous Proofs (with and Appendix by H.L. Pedersen)", by Per Hörfelt, Chalmers University of Technology

PY - 2005

Y1 - 2005

N2 - In this paper, we describe a class of Wiener functionals that are `indeterminate by their moments', that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.

AB - In this paper, we describe a class of Wiener functionals that are `indeterminate by their moments', that is, whose distributions are not uniquely determined by their moments. In particular, it is proved that the integral of a geometric Brownian motion is indeterminate by its moments and, moreover, shown that previous proofs of this result are incorrect. The main result of this paper is based on geometric inequalities in Gauss space and on a generalization of the Krein criterion due to H. L. Pedersen.

KW - Former LIFE faculty

KW - indeterminate moment problem

KW - harmonic function

KW - harmonic estimation

U2 - 10.1239/jap/1127322032

DO - 10.1239/jap/1127322032

M3 - Journal article

SN - 0021-9002

VL - 42

SP - 857

EP - 860

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 3

ER -

The Krein condition for the moment problem: appendix A

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