Clarifications and Corrections to “Random Processes of the Form X_{n=1} = a_{n}X_{n} + b_{n} (mod p) M. Hildebrand, Ann. Probab. 21 (1993) 710-720.

1. On p. 713, in the second line from the bottom insert “0 ≤ c_{1} < 1,” before “k ≠ 0”.

2. On p. 714, in the third line of section 5, condition 2 should be condition 3.

3. On p. 714, in the sixth line of section 5, “nonzero value of b such that P (b_{n} = b) > 0” should be replaced by “nonzero value of b satisfying condition 2”.

4. On p. 714, in the seventh line of section 5, (1 + q^{b(ẽ−d̃)^{k}}) should be (1 + q^{b(ẽ−d̃)k}).

5. On p. 715, the definition of d_{0} should be clarified. In particular,

\begin{aligned}d_{0} & = ∑_{b̃_{1}∈Z} ∑_{b̃_{2}∈Z} P (a_{n} = 1)P (b_{n} = b̃_{1})P (a_{n} = 1)P (b_{n} = b̃_{2}) \\ & = (P (a_{n} = 1))^{2} \end{aligned}

6. In Table 1, there should be vertical dots below the last row shown.

7. On p. 715, 9 lines from the bottom,

max_{k_{0}∈S_{i+1}∪...∪S_{m_{2}} ∪{k:k∉S}} |P̂_{n+mr}(k)|

should be

max_{k_{0}∈S_{i+1}∪...∪S_{m_{2}} ∪{k:k∉S}} |P̂_{n+mr}(k_{0})|

instead.

8. b should be |b| in the last line of p. 714 and in the expression |δ| ≥ 1/(b(ẽ− d̃)) on the 5th line of p. 715.

The author regrets these errors and missed clarifications. The author also thanks Joseph McCollum for helping to point out some difficulties.