Space and time inversions of stochastic processes and Kelvin transform |
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Authors: | L Alili L Chaumont P Graczyk T ak |
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Institution: | L. Alili,L. Chaumont,P. Graczyk,T. ?ak |
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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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Keywords: | diffusion Doob h‐transform inversion Kelvin transform self‐similar Markov processes time change Primary: 31C05 60J45 Secondary: 60J60 60J65 |
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