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This paper studies recurrence properties of autoregressive (AR) processes with `super-heavy-tailed' innovations. Specifically, we study the case where the innovations are distributed, roughly speaking...
Let (M,, SJnao be a Markov random walk whose driving chain (M,JnbwDith general. state space (9,G ) is ergodic with unique stationary distribution 4. Providing n- S, + 0 in probability under PI,it i...
Recurrence of simple random walk on Z2 is dynamically sensitive.
In a first-passage percolation model on the square lattice $Z^2$, if the passage times are independent then the number of geodesics is either $0$ or $+infty$. If the passage times are stationary, ergo...
We review the concept of topological recurrence for weak Feller Markov chains on compact state spaces and explore the implications of this concept for the ergodicity of the processes. We also prove so...
We investigate excited random walks on $Z^d, dge 1,$ and on planar strips $Ztimes{0,1,ldots,L-1}$ which have a drift in a given direction. The strength of the drift may depend on a random i.i.d. envir...
We review the concept of topological recurrence for weak Feller Markov chains on compact state spaces and explore the implications of this concept for the ergodicity of the processes. We also prove so...
We investigate excited random walks on $Z^d, dge 1,$ and on planar strips $Ztimes{0,1,ldots,L-1}$ which have a drift in a given direction. The strength of the drift may depend on a random i.i.d. envir...
The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We re...
This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt = tZt, where the unobservable volatility t ...

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