Konrad Kolesko

activity

20122019

collaborators

5 papers

math.PR2019

Solutions to kinetic-type evolution equations: beyond the boundary case

Dariusz Buraczewski, Konrad Kolesko, Matthias Meiners

We study the asymptotic behavior as $t \to \infty$ of a time-dependent family $(μ_{t})_{t \geq 0}$ of probability measures on $R$ solving the kinetic-type evolution equation…

math.PR2018

Absolute continuity of the martingale limit in branching processes in random environment

Ewa Damek, Nina Gantert, Konrad Kolesko

We consider a supercritical branching process $Z_{n}$ in a stationary and ergodic random environment $ξ = (ξ_{n})_{n \geq 0}$ . Due to the martingale convergence theorem, it is known that th…

math.PR2018

Fluctuations of Biggins' martingales at complex parameters

Alexander Iksanov, Konrad Kolesko, Matthias Meiners

The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The st…

math.PR2017

Stable-like fluctuations of Biggins' martingales

Alexander Iksanov, Konrad Kolesko, Matthias Meiners

Let $(W_{n} (θ))_{n \in N_{0}}$ be Biggins' martingale associated with a supercritical branching random walk, and let $W (θ)$ be its almost sure limit. Under a natural condition…

math.PR2012

Linear stochastic equations in the critical case

Dariusz Buraczewski, Konrad Kolesko

We consider solutions of the stochastic equation $X = d \sum_{i = 1}^{N} A_{i} X_{i} + B$ , where $N$ is a random natural number, $B$ and $A_{i}$ are random positive numbers and $X_i…