Variance properties of sample path derivatives of parametric random variables

Authors:
Jian-Qiang Hu
Affiliations:
Department of Manufacturing Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA
Venue:
Operations Research Letters
Year:
1992

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Abstract

There are many different ways to represent a parametric family of random variables with given marginal probability distributions. These different representations can further give rise to various sample path derivatives. It is therefore natural for us to ask which has better variance properties. In this paper, we give sufficient conditions under which a representation yields a sample path derivative with the smallest variance. We then show that inversion is a representation that usually satisfies these conditions.