Radial Dunkl processes: Existence, uniqueness and hitting time
نویسندگان
چکیده
منابع مشابه
Radial Dunkl Processes : Existence and Uniqueness , Hitting Time , Beta Processes and Random Matrices
Abstract. We begin with the study of some properties of the radial Dunkl process associated to a reduced root system R. It is shown that this diffusion is the unique strong solution for all t ≥ 0 of a SDE with singular drift. Then, we study T0, the first hitting time of the positive Weyl chamber : we prove, via stochastic calculus, a result already obtained by Chybiryakov on the finiteness of T...
متن کاملProcesses : Existence , Uniqueness and Hitting Time
Abstract. 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 t of a stochastic differential equation with a singular drift (see [11] for the original proof and [4] for a proof under an additional restriction), the first hitting time of the Weyl ...
متن کاملFirst Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
Abstract. We provide two equivalent approaches for computing the tail distribution of the first hitting time of the boundary of the Weyl chamber by a radial Dunkl process. The first approach is based on a spectral problem with initial value. The second one expresses the tail distribution by means of the W -invariant Dunkl–Hermite polynomials. Illustrative examples are given by the irreducible r...
متن کاملNote on Radial Dunkl Processes
This note encloses relatively short 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 time t of a stochastic differential equation of a singular drift (see [12] for the original proof and [4] for a proof under additional restrictions), the first hitting time of the ...
متن کاملRadial Dunkl Processes Associated with Dihedral Systems
We give some interest in radial Dunkl processes associated with dihedral systems. We write down the semi group density and as a by-product the generalized Bessel function and the W -invariant generalized Hermite polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chambe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2009
ISSN: 1631-073X
DOI: 10.1016/j.crma.2009.08.003