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Interlacing diffusions

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Assiotis, Theodoros, O’Connell, Neil and Warren, Jon (2019) Interlacing diffusions. In: Donati-Martin , Catherine and Lejay , Antoine and Rouault, Alain, (eds.) Séminaire de Probabilités. Lecture Notes in Mathematics, 2252 . Cham: Springer, pp. 301-380. ISBN 9783030285340

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Official URL: https://doi.org/10.1007/978-3-030-28535-7_13

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Abstract

We study in some generality intertwinings between h-transforms of Karlin-McGregor semigroups associated with one dimensional di.usion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes are interlaced and furthermore give formulae in terms of block determinants for the transition densities of these coupled processes. This allows us to build di.usion processes in the space of Gelfand- Tsetlin patterns so that the evolution of each level is Markovian. We show how known examples naturally fit into this framework and construct new processes related to minors of matrix valued di.usions. We also provide explicit formulae for the transition densities of the particle systems with one-sided collisions at either edge of such patterns.

Item Type: Book Item
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Probabilities, Diffusion -- Statistical methods, Brownian motion processes
Series Name: Lecture Notes in Mathematics
Publisher: Springer
Place of Publication: Cham
ISBN: 9783030285340
ISSN: 0075-8434
Book Title: Séminaire de Probabilités
Editor: Donati-Martin , Catherine and Lejay , Antoine and Rouault, Alain
Official Date: 20 November 2019
Dates:
DateEvent
20 November 2019Available
27 February 2019Accepted
Volume: 2252
Page Range: pp. 301-380
DOI: 10.1007/978-3-030-28535-7_13
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: This is a post-peer-review, pre-copyedit version of an article published in Séminaire de Probabilités. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-28535-7_13
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © Springer Nature Switzerland AG 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
669306European Research Councilhttp://dx.doi.org/10.13039/501100000781
EP/HO23364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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