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Algebraic polynomials and moments of stochastic integrals

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  • Langovoy, Mikhail

Abstract

We propose an algebraic method for proving estimates on moments of stochastic integrals. The method uses qualitative properties of roots of algebraic polynomials from certain general classes. As an application, we give a new proof of a variation of the Burkholder–Davis–Gundy inequality for the case of stochastic integrals with respect to real locally square integrable martingales. Further possible applications and extensions of the method are outlined.

Suggested Citation

  • Langovoy, Mikhail, 2011. "Algebraic polynomials and moments of stochastic integrals," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 627-631.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:6:p:627-631
    DOI: 10.1016/j.spl.2011.01.022
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    References listed on IDEAS

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    1. Nualart, David & Schoutens, Wim, 2000. "Chaotic and predictable representations for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 109-122, November.
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    Cited by:

    1. Qingling Wang, 2017. "Global External Stochastic Stabilization of Linear Systems with Input Saturation: An Alternative Approach," Complexity, Hindawi, vol. 2017, pages 1-7, August.
    2. Novikov, Alexander & Shiryaev, Albert, 2013. "Remarks on moment inequalities and identities for martingales," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1260-1261.

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