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On Convergence to Stochastic Integrals

Author

Listed:
  • Zhengyan Lin

    (Zhejiang University)

  • Hanchao Wang

    (Zhejiang University)

Abstract

Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integrals now plays a major role in modern statistics theory. In this paper, we obtain the weak convergence of various general functionals of partial sums of causal process by means of the method which was introduced in Jacod and Shiryaev (Limit theorems for stochastic processes. Springer, Berlin, 2003).

Suggested Citation

  • Zhengyan Lin & Hanchao Wang, 2016. "On Convergence to Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 29(3), pages 717-736, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0598-8
    DOI: 10.1007/s10959-015-0598-8
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    References listed on IDEAS

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    1. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    2. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.
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    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
    7. Wu, Wei Biao & Shao, Xiaofeng, 2007. "A Limit Theorem For Quadratic Forms And Its Applications," Econometric Theory, Cambridge University Press, vol. 23(5), pages 930-951, October.
    8. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
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