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In this paper we consider the stochastic recurrence equation Y_t=A_tY_t-1+B_t for an i.i.d. sequence of pairs (A_t,B_t) of nonnegative random variables, where we assume that B_t is regularly varying with index κ > 0 and . We show that the stationary solution (Y_t) to this equation has regularly varying finite-dimensional distributions with index κ. This implies that the partial sums of this process are regularly varying. In particular, the relation as x → ∞ holds for some constant . For κ > 1, we also study the large deviation probabilities , for some sequence x_n→ ∞ whose growth depends on the heaviness of the tail of the distribution of Y₁. We show that the relation holds uniformly for x≥ x_n and some constant . Then we apply the large deviation results to derive bounds for the ruin probability …