We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344-353]. It was shown by Key that, under the assumptions made in [Ann.… Expand

For a class of stationary Markov-dependent sequences (A n ,B n ) ∈ R 2 , we consider the random linear recursion S n = A n + B n S n − 1 , n ∈ Z , and show that the distribution tail of its… Expand

We use observed transmission line outage data to make a Markov influence graph that describes the probabilities of transitions between generations of cascading line outages, where each generation of… Expand

This model combines features of several existing models of random motion in random media and admits a transparent physical interpretation, and in the critical (recurrent) regime, generalizes Sinai's scaling of $(\log n)^2$ for the location of the random walk after $n$ steps to $alpha,$ where $\alpha>0$ is a parameter determined by the distribution of the distance between two successive impurities.Expand

We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429-447]. We derive a strong law of large… Expand

The asymptotic properties of the Markov chain are exploited to find the lines most involved in large cascades and show how upgrades to these critical lines can reduce the probability of large cascading lines.Expand

A functional central limit theorem for the biped with an explicit formula for the effective diffusivity coefficient in terms of the parameters of the model is obtained.Expand

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta in 2007. In this paper we study the asymptotic behavior of this model (in particular, weak… Expand