We discuss the joint temporal and contemporaneous aggregation of N independent copies of random-coefficient AR(1) processes driven by independent and identically distributed innovations in the domain of normal attraction of an $\alpha$ -stable distribution, $0< \alpha \le 2$ , as both N and the time scale n tend to infinity, possibly at different rates. Assuming that the tail distribution function of the random autoregressive coefficient regularly varies at the unit root with exponent $\beta > 0$ , we show that, for $\beta < \max (\alpha, 1)$ , the joint aggregate displays a variety of stable and non-stable limit behaviors with stability index depending on $\alpha$ , $\beta$ and the mutual increase rate of N and n. The paper extends the results of Pilipauskaitė and Surgailis (2014) from $\alpha =2$ to $0 < \alpha < 2$ .

We study a random field obtained by counting the number of balls containing a given point when overlapping balls are thrown at random according to a Poisson random measure. We describe a microscopic process which exhibits multifractional behavior. We are particularly interested in the local asymptotic self-similarity (LASS) properties of the field, as well as in its X-ray transform. We obtain two different LASS properties when considering the asymptotics either in law or in the sense of second-order moments, and prove a relationship between the LASS behavior of the field and the LASS behavior of its X-ray transform. These results can be used to model and analyze porous media, images, or connection networks.