Asymptotic behavior of a bilinear model with fractional gaussian noise. Euler’s scheme with small perturbations
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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.
KeywordsErential Equation Fractional Brownian Motion Uniform Norm Memory Property Bilinear Model
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