Limit theorems for auto regression processwith random parameter v, 0 < v < 1

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 ₖₙ ,\; k=1,2,...,n;\; n=1,2,...\ with random coefficients ᵏ ,k∈ N\, generated by the innovation sequence \ξ ₖₙ ,k∈ Z\ 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 \; < \; v<1. In addition, the strong law of large numbers and the law of iterated logarithm are proved.