关于径向Dunkl过程的注记
Note on radial Dunkl processes
摘要：
本文给出了以下已知结果的较短证明：与一个约化系统和一个严格正的重数函数相关联的径向Dunkl过程是一个具有奇异漂移的随机微分方程的所有时间的唯一强解，对于重数函数的小值，径向Dunkl过程到达Weyl腔的首中时几乎必然是有限的.与原来的证明相比，我们的证明提供了更多关于过程行为的信息。更确切地说，第一个证明允许给一个肯定的答案，以猜想宣布的Gallardo和Yor的有限的总长度的跳跃执行的Dunkl过程在有限的时间，而第二个显示，该过程几乎肯定击中墙对应的单根与一个小的多重性值。进一步研究了Dunkl过程的跳跃（D. Lépingle）和其他参考资料包括在内。
英文摘要：
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.
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