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The moment problem for some Wiener functionals: corrections to previous proofs (with an appendix by H. L. Pedersen)

Part of: Markov processes Integral transforms, operational calculus

Published online by Cambridge University Press:  14 July 2016

Per Hörfelt
Per Hörfelt*
Affiliation:
Chalmers University of Technology
*
∗Postal address: Fraunhofer-Chalmers Research Centre for Industrial Mathematics, Chalmers Science Park, SE-412 88 Göteborg, Sweden. Email address: perh@fcc.chalmers.se
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Abstract

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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

Wiener functionalmoment problemgeometric inequality

MSC classification

Primary: 44A60: Moment problems
Secondary: 60J65: Brownian motion
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 851 - 860
Copyright
© Applied Probability Trust 2005 

Footnotes

The author would like to thank Christer Borell, Chalmers University of Technology.

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