[1]
Babillot, M., Bougerol, P. and Elie, L. (1997). The random difference equation *X*
_{
n
} = *A*
_{
n
}
*X*
_{
n-1} + *B*
_{
n
} in the critical case. Ann. Prob.
25, 478–493.

[2]
Bauernschubert, E. (2013). Perturbing transient random walk in a random environment with cookies of maximal strength. Ann. Inst. H. Poincaré Prob. Statist.
49, 638–653.

[3]
Benda, M. (1998). Schwach kontraktive dynamische systeme. Doctoral thesis. Ludwig-Maximilians-Universität München.

[4]
Brofferio, S. (2003). How a centred random walk on the affine group goes to infinity. Ann. Inst. H. Poincaré Prob. Statist.
39, 371–384.

[5]
Brofferio, S. and Buraczewski, D. (2015). On unbounded invariant measures of stochastic dynamical systems. Ann. Prob.
43, 1456–1492.

[6]
Buraczewski, D. (2007). On invariant measures of stochastic recursions in a critical case. Ann. Appl. Prob.
17, 1245–1272.

[7]
Buraczewski, D. and Iksanov, A. (2015). Functional limit theorems for divergent perpetuities in the contractive case. Electron. Commun. Prob.
20, 10.

[8]
Buraczewski, D., Damek, E. and Mikosch, T. (2016). Stochastic Models with Power-Law Tails. The Equation *X* = *AX* + *B*
. Springer, Cham.

[9]
Burton, R. M. and Rösler, U. (1995). An *L*
_{2} convergence theorem for random affine mappings. J. Appl. Prob.
32, 183–192.

[10]
Denisov, D., Korshunov, D. and Wachtel, V. (2016). At the edge of criticality: Markov chains with asymptotically zero drift. Preprint. Available at https://arxiv.org/abs/1612.01592.
[11]
Erickson, K. B. (1973). The strong law of large numbers when the mean is undefined. Trans. Amer. Math. Soc.
185, 371–381.

[12]
Goldie, C. M. and Maller, R. A. (2000). Stability of perpetuities. Ann. Prob.
28, 1195–1218.

[13]
Grincevičius, A. (1976). Limit theorems for products of random linear transformations on the line. Lith. Math. J.
15, 568–579.

[14]
Hitczenko, P. and Wesołowski, J. (2011). Renorming divergent perpetuities. Bernoulli
17, 880–894.

[15]
Iksanov, A. (2016). Renewal Theory for Perturbed Random Walks and Similar Processes. Birkhäuser, Cham.

[16]
Iksanov, A., Pilipenko, A. and Samoilenko, I. (2017). Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the *M*
_{1}-topology. Extremes
20, 567–583.

[18]
Kesten, H. and Maller, R. A. (1996). Two renewal theorems for general random walks tending to infinity. Prob. Theory Relat. Fields
106, 1–38.

[19]
Pakes, A. G. (1983). Some properties of a random linear difference equation. Austral. J. Statist.
25, 345–357.

[20]
Peigné, M. and Woess, W. (2011). Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity. Colloq. Math.
125, 31–54.

[21]
Rachev, S. T. and Samorodnitsky, G. (1995). Limit laws for a stochastic process and random recursion arising in probabilistic modelling. Adv. Appl. Prob.
27, 185–202.

[22]
Stromberg, K. R. (1981). Introduction to Classical Real Analysis. Wadsworth, Belmont, CA.

[23]
Tong, J. C. (1994). Kummer's test gives characterizations for convergence or divergence of all positive series. Amer. Math. Monthly
101, 450–452.

[24]
Zeevi, A. and Glynn, P. W. (2004). Recurrence properties of autoregressive processes with super-heavy-tailed innovations. J. Appl. Prob.
41, 639–653.

[25]
Zerner, M. P. W. (2016). Recurrence and transience of contractive autoregressive processes and related Markov chains. Preprint. Available at https://arxiv.org/abs/1608.01394v2.