5 papers
Large deviations for the maximum of a branching random walk with stretched exponential tails
Piotr Dyszewski, Nina Gantert, Thomas Höfelsauer
We prove large deviation results for the position of the rightmost particle, denoted by , in a one-dimensional branching random walk in a case when Cramér's condition is not s…
Homogeneous mappings of regularly varying vectors
Piotr Dyszewski, Thomas Mikosch
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provi…
Random walks in a strongly sparse random environment
Dariusz Buraczewski, Piotr Dyszewski, Alexander Iksanov +1
The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depe…
Precise large deviations for random walk in random environment
Dariusz Buraczewski, Piotr Dyszewski
We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random…
Iterated random functions and regularly varying tails
Ewa Damek, Piotr Dyszewski
We consider solutions to so-called stochastic fixed point equation , where is a random Lipschitz function and is a random variable independent of $Ψ…