关于各向异性稳定的JCIR过程
On the anisotropic stable JCIR process
摘要：
我们研究了各向异性稳定JCIR过程，它是稳定JCIR过程的多维扩展，也是经典JCIR过程的多维模拟。证明了各向异性稳定JCIR过程的热核存在，且在加权各向异性Besov范数下满足先验界。在此基础上，我们推出了强Feller性质，并证明了，在次临界情况下，指数遍历全变差。此外，我们表明，在一维的情况下，相应的热核是光滑的。
英文摘要：
We investigate the anisotropic stable JCIR process which is a multi-dimensional extension of the stable JCIR process but also a multi-dimensional analogue of the classical JCIR process. We prove that the heat kernel of the anisotropic stable JCIR process exists and it satisfies an a-priori bound in a weighted anisotropic Besov norm. Based on this regularity result we deduce the strong Feller property and prove, for the subcritical case, exponential ergodicity in total variation. Also, we show that in the one-dimensional case the corresponding heat kernel is smooth.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
