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

Martin Friesen, Peng Jin and Barbara Rüdiger

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5426-5452

Abstract: 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.

Keywords: Multi-type continuous-state branching processes with immigration; Affine processes; Density; Anisotropic Besov space (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.03.012

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