O‘zbekiston matematika jurnali 69-том 3-нөмір (2025) · 176-180-беттер
Limit theorems for auto regression processwith random parameter v, 0 < v < 1
T.M.Zuparov, A.I.Jovliev
Аңдатпа
In this paper we obtain the criterion of weak convergence of the sequence of the sum of the first $n$ terms of the linear process $\left\{X_{kn} ,\; k=1,2,...,n;\; n=1,2,...\right\}$ with random coefficients $\left\{v^{k} ,k\in {\mathbb N}\right\}$, generated by the innovation sequence $\left\{\xi _{kn} ,k\in Z\right\}$ satisfying the condition of infinite smallness to the limit distribution and as a consequence of this result we obtain the analog of the Lindeberg-Feller theorem for the auto regression process with random parameter $v,\; 0{\rm \; }<{\rm \; }v<1$. In addition, the strong law of large numbers and the law of iterated logarithm are proved.
Auto regression process, linear process, central limit theorem, strong law of large numbers, law of iterated logarithm
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