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Stochastic equations for two-type continuous-state branching processes with immigration

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Abstract

A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.

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References

  1. Jiřina, M.: Stochastic branching processes with continuous state space. Czech. Math. J., 8, 292–313 (1958)

    Google Scholar 

  2. Lamperti, J.: Continuous state branching processes. Bull. Amer. Math. Soc., 73, 382–386 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  3. Caballero, M. E., Lambert, A., Uribe Bravo, G.: Proof(s) of the Lamperti representation of continuous-state branching processes. Probab. Surv., 6, 62–89 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Watanabe, S.: On two dimensional Markov processes with branching property. Trans. Amer. Math. Soc., 136, 447–466 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kawazu, K., Watanabe, S.: Branching processes with immigration and related limit theorems. Theory Probab. Appl., 16, 36–54 (1971)

    Article  MathSciNet  Google Scholar 

  6. Dawson, D. A., Li, Z. H.: Skew convolution semigroups and affine Markov processes. Ann. Probab., 34, 1103–1142 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fu, Z. F., Li, Z. H.: Stochastic equations of non-negative processes with jumps. Stochastic Process. Appl., 120, 306–330 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, Z. H.: Measure-valued Branching Markov Processes, Springer, Berlin, 2011

    Book  MATH  Google Scholar 

  9. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, North-Holland/Kodansha, Amsterdam/Tokyo, 1989

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Ru Gang Ma

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  1. Ru Gang Ma
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Correspondence to Ru Gang Ma.

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Ma, R.G. Stochastic equations for two-type continuous-state branching processes with immigration. Acta. Math. Sin.-English Ser. 29, 287–294 (2013). https://doi.org/10.1007/s10114-012-1378-3

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  • DOI: https://doi.org/10.1007/s10114-012-1378-3

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