Independence by Random Scaling

2017/03/06 by James, Lancelot F., Orbanz, Peter
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1703.02054

Abstract

We give conditions under which a scalar random variable T can be coupled to a random scaling factor ξ such that T and ξT are rendered stochastically independent. A similar result is obtained for random measures. One consequence is a generalization of a result by Pitman and Yor on the Poisson-Dirichlet distribution to its negative parameter range. Another application are diffusion excursions straddling an exponential random time.

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