Invariance principle in a bilinear model with weak nonlinearity |
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Authors: | M. A. Lifshits |
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Affiliation: | (1) St. Petersburg State University, St. Petersburg, Russia |
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Abstract: | We consider a series of bilinear sequences , with i.i.d. εk and small bilinearity coefficients bn = βn−1/2 and show that under the standard normalization they converge to a diffusion process Yβ. We provide an explicit form of Yβ, investigate the moments of Yβ, 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. |
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