Existence of densities for multitype CBI processes
Abstract
Let X be a multitype continuousstate branching process with immigration (CBI process) on state space $\mathbb{R}^d$. Denote by $g_t$, $t \geq 0$, the law of $X_{t}$. We provide sufficient conditions under which $g_t$ has, for each $t > 0$, a density with respect to the Lebesgue measure. Such density has, by construction, some anisotropic Besov regularity. Our approach neither relies on the use of Malliavin calculus nor on the study of corresponding Laplace transform.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 DOI:
 10.48550/arXiv.1810.00400
 arXiv:
 arXiv:1810.00400
 Bibcode:
 2018arXiv181000400F
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 60E07;
 60G30;
 60J80
 EPrint:
 Stochastic Processes and their Applications Volume 130, Issue 9, September 2020, Pages 54265452