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On Convergence to Stochastic Integrals

Author

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  • 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

    as
    1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    2. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    3. 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.
    4. 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.
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    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. 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.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    Full references (including those not matched with items on IDEAS)

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