On the anisotropic stable JCIR process

2019/08/15 by Martin Friesen, Peng Jin, Friesen, Martin +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #37A25 #60J25 #FOS: Mathematics #Primary 60H10 #Probability (math.PR) #Probability and Risk Models #Secondary 60J35 #Statistical Methods and Inference #Stochastic processes and financial applications #math.PR #msc:37A25 #msc:60H10 #msc:60J25 #msc:60J35

paper · pdf · doi:10.48550/arxiv.1908.05473

30 pages

arxiv created 2019/08/15 · openalex publication_date 2019/08/15 · arxiv updated 2019/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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