@inbook{48341cd662134f039d7ef3dad3aa439f,

title = "Oscillatory Attraction and Repulsion from a Subset of the Unit Sphere or Hyperplane for Isotropic Stable L{\'e}vy Processes",

abstract = "Suppose that S is a closed set of the unit sphere Sd−1 = {x ∈ Rd : |x| = 1} in dimension d ≥ 2, which has positive surface measure. We construct the law of absorption of an isotropic stable L{\'e}vy process in dimension d ≥ 2 conditioned to approach S continuously, allowing for the interior and exterior of Sd−1 to be visited infinitely often. Additionally, we show that this process is in duality with the unconditioned stable L{\'e}vy process. We can replicate the aforementioned results by similar ones in the setting that S is replaced by D, a closed bounded subset of the hyperplane {x ∈ Rd : (x, v) = 0} with positive surface measure, where v is the unit orthogonal vector and where (·, ·) is the usual Euclidean inner product. Our results complement similar results of the authors [17] in which the stable process was further constrained to attract to and repel from S from either the exterior or the interior of the unit sphere.",

keywords = "Duality, Stable process, Time reversal",

author = "Mateusz Kwa{\'s}nicki and Kyprianou, {Andreas E.} and Sandra Palau and Tsogzolmaa Saizmaa",

note = "Funding Information: Acknowledgments TS acknowledges support from a Schlumberger Faculty of the Future award. SP acknowledges support from the Royal Society as a Newton International Fellow Alumnus (AL201023) and UNAM-DGAPA-PAPIIT grant no. IA103220. Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",

year = "2021",

month = jul,

day = "30",

doi = "10.1007/978-3-030-83309-1_16",

language = "English",

isbn = "9783030833084",

series = "Progress in Probability",

publisher = "Birkhauser",

pages = "283--313",

editor = "{Chaumont }, L. and Kyprianou, {A. E.}",

booktitle = "A Lifetime of Excursions Through Random Walks and L{\'e}vy Processes",

}