2008/12/22 by Nizar Demni, Demni, Nizar · 1 citation
Mathematics · Physics and Astronomy · #60G18 #60H10 #60J60 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #math.PR #msc:60G18 #msc:60H10 #msc:60J60
paper · pdf · doi:10.48550/arxiv.0812.4269
Further results on jumps and additional references are included. arXiv admin note: substantial text overlap with arXiv:0812.4315
openalex publication_date 2008/12/22 · arxiv created 2012/03/18 · arxiv updated 2012/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give shorter proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all times of a stochastic differential equation with a singular drift, the first hitting time of the Weyl chamber by a radial Dunkl process is finite almost surely for small values of the multiplicity function. Compared to the original proofs, ours give more information on the behavior of the process. More precisely, the first proof allows to give a positive answer to a conjecture announced by Gallardo and Yor for the finiteness of the total length of the jumps performed by the Dunkl process during a finite amount of time, while the second one shows that the process hits almost surely the wall corresponding to the simple root with a small multiplicity value. Further results on the jumps of the Dunkl process (communicated by D. Lépingle) and and additional references are included.