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SPACE AND TIME INVERSIONS OF STOCHASTIC PROCESSES AND KELVIN TRANSFORM

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.
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https://hal.archives-ouvertes.fr/hal-01505747
Contributor : Piotr Graczyk Connect in order to contact the contributor
Submitted on : Tuesday, April 11, 2017 - 5:10:34 PM
Last modification on : Wednesday, November 3, 2021 - 6:05:20 AM
Long-term archiving on: : Wednesday, July 12, 2017 - 1:34:02 PM

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  • HAL Id : hal-01505747, version 1

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L Alili, L Chaumont, P Graczyk, T ˙ Zak. SPACE AND TIME INVERSIONS OF STOCHASTIC PROCESSES AND KELVIN TRANSFORM. 2017. ⟨hal-01505747⟩

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