2019/11/13 by Andreas E. Kyprianou, Kyprianou, Andreas E., Sandra Palau +3
Economics, Econometrics and Finance · Mathematics · #60E10 #60J80 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1911.05867
openalex publication_date 2019/11/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Taking account of recent developments in the representation of\nd-dimensional isotropic stable L 'evy processes as self-similar Markov\nprocesses, we consider a number of new ways to condition its path. Suppose that\n\Ω is a region of the unit sphere mathbbSd-1 = x\∈\n\ℝd: |x| =1 . We construct the aforesaid stable L 'evy process\nconditioned to approach \S continuously from either inside or outside\nof the sphere. Additionally, we show that %this these processes are in duality\nwith the stable process conditioned to remain inside the sphere and absorb\ncontinuously at the origin and to remain outside of the sphere, respectively.\nOur results extend the recent contributions of D "oring and Weissman (2018),,\nwhere similar conditioning is considered, albeit in one dimension. As is the\ncase there, we appeal to recent fluctuation identities related to the deep\nfactorisation of stable processes.\n