Attraction to and repulsion from patches on the hypersphere and hyperplane for isotropic d-dimensional α-stable processes with index in α ∈ (0, 1] and d ≥ 2

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• Andreas Kyprianou (University of Bath)
• Friday 22 April 2022, 10:00-11:00
• Seminar Room 1, Newton Institute.

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FD2W03 - Optimal control and fractional dynamics

Consider a d-dimensional α-stable processes with index in α∈(0,1) and d≥2. Suppose that Ω is a region of the unit sphere S ^{= {x ∈ R}d : |x| = 1}. We construct the aforesaid stable Lévy process conditioned to approach Ω continuously, either from inside S^{, from outside S}{d−1} or in an oscillatory way; all of which have zero probability. Our approach also extends to the setting of hitting bounded domains of (d-1)-dimensional hyperplanes. We appeal to a mixture of methods, appealing to the modern theory of self-similar Markov process as well as the classical potential analytic view. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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