Independence by Random Scaling

Lancelot F. James; Peter Orbanz

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arXiv · 1703.02054

Independence by Random Scaling

Lancelot F. James·Peter Orbanz

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Abstract

We give conditions under which a scalar random variable T can be coupled to a random scaling factor $\xi$ such that T and $\xi$T 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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Lancelot F. James, Peter Orbanz. 2017-03-06. Independence by Random Scaling. https://arxiv.org/abs/1703.02054

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