Existence of densities for multi-type continuous-state branching processes with immigration

Let X be a multi-type continuous-state branching process with immigration on state space R+d. Denote by gt, t≥0, the law of X(t). We provide sufficient conditions under which gt has, for each t>0, a density with respect to the Lebesgue measure. Such density has, by construction, some Besov regula...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 130; no. 9; pp. 5426 - 5452
Main Authors Friesen, Martin, Jin, Peng, Rüdiger, Barbara
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2020
Subjects
Affine processes
Anisotropic Besov space
Density
Multi-type continuous-state branching processes with immigration
Multi-type continuous-state branching processes with immigration
Affine processes
60G30
60J80
Anisotropic Besov space
60E07
Density
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ISSN0304-4149
1879-209X
DOI10.1016/j.spa.2020.03.012

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Summary:Let X be a multi-type continuous-state branching process with immigration on state space R+d. Denote by gt, t≥0, the law of X(t). We provide sufficient conditions under which gt has, for each t>0, a density with respect to the Lebesgue measure. Such density has, by construction, some Besov regularity. Our approach is based on a discrete integration by parts formula combined with a precise estimate on the error of the one-step Euler approximations of the process. As an auxiliary result, we also provide a criterion for the existence of densities of solutions to a general stochastic equation driven by Brownian motions and Poisson random measures, whose coefficients are Hölder continuous and might be unbounded.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2020.03.012