Journal of Mathematical Sciences

, Volume 147, Issue 4, pp 6847–6863 | Cite as

Asymptotic behavior of a bilinear model with fractional gaussian noise. Euler’s scheme with small perturbations



We consider the Unit Root Bilinear model with a sequence of innovations given by a fractional Gaussian noise (increases of a fractional Brownian motion). For such a model, we prove a variant of the Donsker-Prokhorov limit theorem and establish the convergence of the model in probability to a solution of a proper stochastic differential equation with FBM. The proof is based on a result on convergence of the Euler’s scheme with “small perturbations” for SDE with FBM, which is also proved. Bibliography: 20 titles.


Erential Equation Fractional Brownian Motion Uniform Norm Memory Property Bilinear Model 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Kiev National UniversityKievUkraine

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