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Weak approximation for a class of Gaussian processes. (English) Zbl 0968.60008

The authors prove that, under rather general conditions, the law of a continuous Gaussian process represented by a stochastic integral of a deterministic kernel, with respect to a standard Wiener process, can be weakly approximated by the law of some processes constructed from a standard Poisson process. An example of a Gaussian process to which this result applies is the fractional Brownian motion with any Hurst parameter. The fractional Brownian motion was introduced by B. B. Mandelbrot and J. W. Van Ness [SIAM Rev. 10, 422-437 (1968; Zbl 0179.47801)] and is generally considered as a good model in many applications in engineering, economics, physics and biology, for example, due to its long-term dependence and selfsimilarity character.

MSC:

60B10 Convergence of probability measures
60F17 Functional limit theorems; invariance principles

Citations:

Zbl 0179.47801
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