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Diffusion approximation of normalized integrals of weakly dependent processes and its applications

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Abstract

We obtain exact estimates for the rate of convergence of normalized integrals of weakly dependent stationary processes to the standard Wiener process in the uniform metric in probability. These estimates are then applied to the investigation of the behavior of stochastic systems with curvilinear boundaries subjected to the action of weakly dependent random perturbations.

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Authors and Affiliations

  1. Donetsk University, Donetsk

    B. V. Bondarev & I. L. Shurko

Authors
  1. B. V. Bondarev
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  2. I. L. Shurko
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Additional information

Translated from Ukrainskii Matematicheskii Zhumal, Vol.46, No. 11, pp. 1449–1466, November, 1994.

The present work was performed as a part of Project No. 8 of the Ministry of Education of the Ukraine. The manager of the project is Prof. N. A. Perestyuk.

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Bondarev, B.V., Shurko, I.L. Diffusion approximation of normalized integrals of weakly dependent processes and its applications. Ukr Math J 46, 1600–1619 (1994). https://doi.org/10.1007/BF01058879

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  • DOI: https://doi.org/10.1007/BF01058879

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