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

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  • Friesen, Martin
  • Jin, Peng
  • Rüdiger, Barbara

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.

Suggested Citation

  • Friesen, Martin & Jin, Peng & Rüdiger, Barbara, 2020. "Existence of densities for multi-type continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5426-5452.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5426-5452
    DOI: 10.1016/j.spa.2020.03.012
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    References listed on IDEAS

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    Cited by:

    1. Martin Friesen & Peng Jin, 2022. "Volterra square-root process: Stationarity and regularity of the law," Papers 2203.08677, arXiv.org, revised Oct 2022.

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