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Localization of Wiener functionals of fractional regularity and applications

Author

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  • He, Kai
  • Ren, Jiagang
  • Zhang, Hua

Abstract

In this paper we localize some of Watanabe’s results on Wiener functionals of fractional regularity, and use them to give a precise estimate of the difference between two Donsker’s delta functionals even with fractional differentiability. As an application, the convergence rate of the density of the Euler scheme for non-Markovian stochastic differential equations is obtained.

Suggested Citation

  • He, Kai & Ren, Jiagang & Zhang, Hua, 2014. "Localization of Wiener functionals of fractional regularity and applications," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2543-2582.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2543-2582
    DOI: 10.1016/j.spa.2014.03.010
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    References listed on IDEAS

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    1. Bally, Vlad & Caramellino, Lucia, 2011. "Riesz transform and integration by parts formulas for random variables," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1332-1355, June.
    2. BALLY Vlad & TALAY Denis, 1996. "The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density," Monte Carlo Methods and Applications, De Gruyter, vol. 2(2), pages 93-128, December.
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    Cited by:

    1. Guilan Cao & Kai He, 2021. "Estimates of the Difference Between Two Probability Densities of Wiener Functionals and Its Application," Journal of Theoretical Probability, Springer, vol. 34(2), pages 553-579, June.

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