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    Matrix dufresne identities

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    Genre
    Journal Article
    Date
    2016-01-01
    Author
    Rider, B
    Valkó, B
    Subject
    math.PR
    math.PR
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5797
    
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    DOI
    10.1093/imrn/rnv127
    Abstract
    © The Author(s) 2015. Published by Oxford University Press. We prove a version of the classical Dufresne identity for matrix processes. More specifically, we show that the inverse Wishart laws on the space of positive definite r × r matrices can be realized by ∫∞0 MsMTs ds in which t →MT is a drifted Brownian motion on GLr(ℝ). This solves a problem in the study of spiked random matrix ensembles which served as the original motivation for this result. Various known extensions of the Dufresne identity (and their applications) are also shown to have analogs in this setting. In particular, we identify matrix-valued diffusions built from Mt which generalize in a natural way the scalar processes figuring into the geometric L'evy and Pitman theorems of Matsumoto and Yor.
    Citation to related work
    Oxford University Press (OUP)
    Has part
    International Mathematics Research Notices
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5779
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