Geodesic
Asymptotic behavior of the Unit Root Bilinear
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 5-33

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We consider the Unit Root Bilinear model with a sequence of innovations given by the fractional Gaussian noise (increases of the fractional Brownian motion). For such a model we prove a variant of the Donsker–Prohorov limit theorem and obtain convergence of the model in probability to solution of a proper stochastic differential equation with fBm. The proof is based on the result about convergence of the Euler's scheme with ‘small perturbations’ for SDE with fBm, which is also proved. 
@article{ZNSL_2007_341_a0,
     author = {T. Androshchuk},
     title = {Asymptotic behavior of the {Unit} {Root} {Bilinear}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--33},
     publisher = {mathdoc},
     volume = {341},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a0/}
}
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T. Androshchuk. Asymptotic behavior of the Unit Root Bilinear. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 5-33. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a0/