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Space and time inversions of stochastic processes and Kelvin transform
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Alili, Larbi, Chaumont, L., Graczyk, P. and Żak, T. (2019) Space and time inversions of stochastic processes and Kelvin transform. Mathematische Nachrichten, 292 (2). pp. 252-272. doi:10.1002/mana.201700152 ISSN 0025-584X.
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Official URL: https://doi.org/10.1002/mana.201700152
Abstract
Let X be a standard Markov process. We prove that a space inversion property of X implies the existence of a Kelvin transform of X‐harmonic, excessive and operator‐harmonic functions and that the inversion property is inherited by Doob h‐transforms. We determine new classes of processes having space inversion properties amongst transient processes satisfying the time inversion property. For these processes, some explicit inversions, which are often not the spherical ones, and excessive functions are given explicitly. We treat in details the examples of free scaled power Bessel processes, non‐colliding Bessel particles, Wishart processes, Gaussian Ensemble and Dyson Brownian Motion.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Journal or Publication Title: | Mathematische Nachrichten | ||||||||
| Publisher: | Wiley | ||||||||
| ISSN: | 0025-584X | ||||||||
| Official Date: | February 2019 | ||||||||
| Dates: |
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| Volume: | 292 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 252-272 | ||||||||
| DOI: | 10.1002/mana.201700152 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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