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Exact parabolic asymptotics for singular -D Burgers' random fields: Gaussian approximation

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  • Leonenko, N. N.
  • Woyczynski, W. A.

Abstract

The rate of convergence (in the uniform Kolmogorov's distance) for probability distributions of parabolically rescaled solutions of the multidimensional Burgers' equation with random singular Gaussian initial data (with long-range dependence) to a limit Gaussian random field is discussed in this paper.

Suggested Citation

  • Leonenko, N. N. & Woyczynski, W. A., 1998. "Exact parabolic asymptotics for singular -D Burgers' random fields: Gaussian approximation," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 141-165, August.
    • Handle: RePEc:eee:spapps:v:76:y:1998:i:2:p:141-165
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    References listed on IDEAS

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    1. Hodges, Stewart & Carverhill, Andrew, 1993. "Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing," Economic Journal, Royal Economic Society, vol. 103(417), pages 395-405, March.
    2. Hu, Y. M. & Woyczynski, W. A., 1995. "Limit Behavior of Quadratic Forms of Moving Averages and Statistical Solutions of the Burgers' Equation," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 15-44, January.
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    Cited by:

    1. Nikolai Leonenko & Emanuele Taufer, 2001. "On the rate of convergence to the Normal approximation of LSE in multiple regression with long memory random fields," Quaderni DISA 044, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    2. Anh, V. V. & Leonenko, N. N., 1999. "Non-Gaussian scenarios for the heat equation with singular initial conditions," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 91-114, November.

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