1 Department of Natural Sciences, Department of Basic Sciences and Environment, Faculty of Life Sciences, Københavns Universitet2 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
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.
Journal of Applied Probability, 2005, Vol 42, Issue 3, p. 857-860
LIFE; indeterminate moment problem; harmonic function; harmonic estimation