Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes

Andreas E. Kyprianou, Sandra Palau and Tsogzolmaa Saizmaa

Stochastic Processes and their Applications, 2021, vol. 137, issue C, 272-293

Abstract: Taking account of recent developments in the representation of d-dimensional isotropic stable Lévy processes as self-similar Markov processes, we consider a number of new ways to condition its path. Suppose that S is a region of the unit sphere Sd−1={x∈Rd:|x|=1}. We construct the aforesaid stable Lévy process conditioned to approach S continuously from either inside or outside of the sphere. Additionally, we show that these processes are in duality with the stable process conditioned to remain inside the sphere and absorb continuously at the origin and to remain outside of the sphere, respectively. Our results extend the recent contributions of Döring and Weissman (2020), where similar conditioning is considered, albeit in one dimension as well as providing analogues of the same classical results for Brownian motion, cf. Doob (1957). As in Döring and Weissman (2020), we appeal to recent fluctuation identities related to the deep factorisation of stable processes, cf. Kyprianou (2016), Kyprianou et al. (2020) and Kyprianou et al. (2017).

Keywords: Stable process; Radial excursion; Time reversal; Duality (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S030441492100051X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:137:y:2021:i:c:p:272-293

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2021.04.004

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().