Weak approximation for a class of gaussian processes

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Abstract

We prove that, under rather general conditions, the law of a continuousGaussian 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. © 2000 Applied Probability Trust.
Original languageEnglish
Pages (from-to)400-407
JournalJournal of Applied Probability
Volume37
Issue number2
DOIs
Publication statusPublished - 1 Jan 2000

Keywords

  • Fractional Brownian motion
  • Gaussian process
  • Poisson process
  • Weak convergence

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