Invariance principle in a bilinear model with weak nonlinearity

We consider a series of bilinear sequences , with i.i.d. ε_k and small bilinearity coefficients b_n = βn^−1/2 and show that under the standard normalization they converge to a diffusion process Y_β. We provide an explicit form of Y_β, investigate the moments of Y_β, and study the limiting behavior of some other quantities related to X _k ⁽ⁿ⁾ and important for statistical applications. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 97–105.