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A Weak Convergence to Hermite Process by Martingale Differences

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  • Xichao Sun
  • Ronglong Cheng

Abstract

We consider the weak convergence to general Hermite process ZH,k of order k with index H. By applying martingale differences we construct a sequence {ZH, kn , n=1,2,…} of multiple Wiener‐Itô stochastic integrals such that it converges in distribution to the Hermite process ZH,k.

Suggested Citation

  • Xichao Sun & Ronglong Cheng, 2014. "A Weak Convergence to Hermite Process by Martingale Differences," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:307819
    DOI: 10.1155/2014/307819
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    References listed on IDEAS

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    1. Nieminen, Ari, 2004. "Fractional Brownian motion and Martingale-differences," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 1-10, October.
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    Cited by:

    1. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.

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