Existence of densities for multi-type CBI processes

Abstract

Let X be a multi-type continuous-state branching process with immigration (CBI process) on state space ${\mathbb{R}}^d$. Denote by $g_t$, $t\ge 0$, 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.

References in corpus (3)

• On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes
• Boundary behavior of multi-type continuous-state branching processes with immigration
• On the anisotropic stable JCIR process

Cited by in corpus (4)

• Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
• Boundary behavior of multi-type continuous-state branching processes with immigration
• Regularity of transition densities and ergodicity for affine jump-diffusion processes
• Distributional properties of jumps of multi-type CBI processes