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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
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 | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| 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: |
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| 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: |
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