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Moment Formulas for Multitype Continuous State and Continuous Time Branching Process with Immigration

Author

Listed:
  • Mátyás Barczy

    (University of Debrecen)

  • Zenghu Li

    (Beijing Normal University)

  • Gyula Pap

    (University of Szeged)

Abstract

Recursions for moments of multitype continuous state and continuous time branching process with immigration are derived. It turns out that the $$k$$ k th (mixed) moments and the $$k$$ k th (mixed) central moments are polynomials of the initial value of the process, and their degree is at most $$k$$ k and $$\lfloor k/2 \rfloor $$ ⌊ k / 2 ⌋ , respectively.

Suggested Citation

  • Mátyás Barczy & Zenghu Li & Gyula Pap, 2016. "Moment Formulas for Multitype Continuous State and Continuous Time Branching Process with Immigration," Journal of Theoretical Probability, Springer, vol. 29(3), pages 958-995, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0605-0
    DOI: 10.1007/s10959-015-0605-0
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    References listed on IDEAS

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    1. Mátyás Barczy & Márton Ispány & Gyula Pap, 2014. "Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 866-892, December.
    2. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    3. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    4. Mátyás Barczy & Zenghu Li & Gyula Pap, 2015. "Yamada-Watanabe Results for Stochastic Differential Equations with Jumps," International Journal of Stochastic Analysis, Hindawi, vol. 2015, pages 1-23, January.
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    Cited by:

    1. Shukai Chen, 2023. "On the Exponential Ergodicity of (2+2)-Affine Processes in Total Variation Distances," Journal of Theoretical Probability, Springer, vol. 36(1), pages 315-330, March.

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